diff --git a/include/xrpl/basics/Number.h b/include/xrpl/basics/Number.h
index 2f467fb036b..8d91fbe05e8 100644
--- a/include/xrpl/basics/Number.h
+++ b/include/xrpl/basics/Number.h
@@ -10,6 +10,10 @@
 #include <ostream>
 #include <string>
 
+#ifdef _MSC_VER
+#include <boost/multiprecision/cpp_int.hpp>
+#endif  // !defined(_MSC_VER)
+
 namespace xrpl {
 
 class Number;
@@ -17,18 +21,37 @@ class Number;
 std::string
 to_string(Number const& amount);
 
+/** Returns a rough estimate of log10(value).
+ *
+ * The return value is a pair (log, rem), where log is the estimated log10,
+ * and rem is value divided by 10^log. If rem is 1, then value is an exact
+ * power of ten, and log is the exact log10(value).
+ *
+ * This function only works for positive values.
+ */
 template <typename T>
-constexpr std::optional<int>
-logTen(T value)
+constexpr std::pair<int, T>
+logTenEstimate(T value)
 {
     int log = 0;
-    while (value >= 10 && value % 10 == 0)
+    T remainder = value;
+    while (value >= 10)
     {
+        if (value % 10 == 0)
+            remainder = remainder / 10;
         value /= 10;
         ++log;
     }
-    if (value == 1)
-        return log;
+    return {log, remainder};
+}
+
+template <typename T>
+constexpr std::optional<int>
+logTen(T value)
+{
+    auto const est = logTenEstimate(value);
+    if (est.second == 1)
+        return est.first;
     return std::nullopt;
 }
 
@@ -42,12 +65,10 @@ isPowerOfTen(T value)
 /** MantissaRange defines a range for the mantissa of a normalized Number.
  *
  * The mantissa is in the range [min, max], where
- * * min is a power of 10, and
- * * max = min * 10 - 1.
  *
  * The mantissa_scale enum indicates whether the range is "small" or "large".
  * This intentionally restricts the number of MantissaRanges that can be
- * instantiated to two: one for each scale.
+ * used to two: one for each scale.
  *
  * The "small" scale is based on the behavior of STAmount for IOUs. It has a min
  * value of 10^15, and a max value of 10^16-1. This was sufficient for
@@ -61,8 +82,8 @@ isPowerOfTen(T value)
  * "large" scale.
  *
  * The "large" scale is intended to represent all values that can be represented
- * by an STAmount - IOUs, XRP, and MPTs. It has a min value of 10^18, and a max
- * value of 10^19-1.
+ * by an STAmount - IOUs, XRP, and MPTs. It has a min value of 2^63/10+1
+ * (truncated), and a max value of 2^63-1.
  *
  * Note that if the mentioned amendments are eventually retired, this class
  * should be left in place, but the "small" scale option should be removed. This
@@ -74,28 +95,50 @@ struct MantissaRange
     enum mantissa_scale { small, large };
 
     explicit constexpr MantissaRange(mantissa_scale scale_)
-        : min(getMin(scale_))
-        , max(min * 10 - 1)
-        , log(logTen(min).value_or(-1))
+        : max(getMax(scale_))
+        , min(computeMin(max))
+        , referenceMin(getReferenceMin(scale_, min))
+        , log(computeLog(min))
         , scale(scale_)
     {
+        // Since this is constexpr, if any of these throw, it won't compile
+        if (min * 10 <= max)
+            throw std::out_of_range("min * 10 <= max");
+        if (max / 10 >= min)
+            throw std::out_of_range("max / 10 >= min");
+        if ((min - 1) * 10 > max)
+            throw std::out_of_range("(min - 1) * 10 > max");
+        // This is a little hacky
+        if ((max + 10) / 10 < min)
+            throw std::out_of_range("(max + 10) / 10 < min");
     }
 
-    rep min;
+    // Explicitly delete copy and move operations
+    MantissaRange(MantissaRange const&) = delete;
+    MantissaRange(MantissaRange&&) = delete;
+    MantissaRange&
+    operator=(MantissaRange const&) = delete;
+    MantissaRange&
+    operator=(MantissaRange&&) = delete;
+
     rep max;
+    rep min;
+    // This is not a great name. Used to determine if mantissas are in range,
+    // but have fewer digits than max
+    rep referenceMin;
     int log;
     mantissa_scale scale;
 
 private:
     static constexpr rep
-    getMin(mantissa_scale scale_)
+    getMax(mantissa_scale scale)
     {
-        switch (scale_)
+        switch (scale)
         {
             case small:
-                return 1'000'000'000'000'000ULL;
+                return 9'999'999'999'999'999ULL;
             case large:
-                return 1'000'000'000'000'000'000ULL;
+                return std::numeric_limits<std::int64_t>::max();
             default:
                 // Since this can never be called outside a non-constexpr
                 // context, this throw assures that the build fails if an
@@ -103,6 +146,33 @@ struct MantissaRange
                 throw std::runtime_error("Unknown mantissa scale");
         }
     }
+
+    static constexpr rep
+    computeMin(rep max)
+    {
+        return max / 10 + 1;
+    }
+
+    static constexpr rep
+    getReferenceMin(mantissa_scale scale, rep min)
+    {
+        switch (scale)
+        {
+            case large:
+                return 1'000'000'000'000'000'000ULL;
+            default:
+                if (isPowerOfTen(min))
+                    return min;
+                throw std::runtime_error("Unknown/bad mantissa scale");
+        }
+    }
+
+    static constexpr rep
+    computeLog(rep min)
+    {
+        auto const estimate = logTenEstimate(min);
+        return estimate.first + (estimate.second == 1 ? 0 : 1);
+    }
 };
 
 // Like std::integral, but only 64-bit integral types.
@@ -110,6 +180,24 @@ template <class T>
 concept Integral64 =
     std::is_same_v<T, std::int64_t> || std::is_same_v<T, std::uint64_t>;
 
+template <class STAmount, class Asset>
+concept CanUseAsScale = requires(Asset a, Number n) { STAmount(a, n); } &&
+    requires(STAmount s) { s.exponent(); };
+
+namespace detail {
+#ifdef _MSC_VER
+using uint128_t = boost::multiprecision::uint128_t;
+using int128_t = boost::multiprecision::int128_t;
+#else   // !defined(_MSC_VER)
+using uint128_t = __uint128_t;
+using int128_t = __int128_t;
+#endif  // !defined(_MSC_VER)
+
+template <class T>
+concept UnsignedMantissa =
+    std::is_unsigned_v<T> || std::is_same_v<T, uint128_t>;
+}  // namespace detail
+
 /** Number is a floating point type that can represent a wide range of values.
  *
  * It can represent all values that can be represented by an STAmount -
@@ -137,9 +225,7 @@ concept Integral64 =
  *   1. Normalization can be disabled by using the "unchecked" ctor tag. This
  *      should only be used at specific conversion points, some constexpr
  *      values, and in unit tests.
- *   2. The max of the "large" range, 10^19-1, is the largest 10^X-1 value that
- *      fits in an unsigned 64-bit number. (10^19-1 < 2^64-1 and
- *      10^20-1 > 2^64-1). This avoids under- and overflows.
+ *   2. The max of the "large" range, 2^63-1, TODO: explain the large range.
  *
  * ---- External Interface ----
  *
@@ -153,7 +239,7 @@ concept Integral64 =
  *
  * Note:
  *   1. 2^63-1 is between 10^18 and 10^19-1, which are the limits of the "large"
- *      mantissa range.
+ *      mantissa range. TODO: update this explanation.
  *   2. The functions mantissa() and exponent() return the external view of the
  *      Number value, specifically using a signed 63-bit mantissa. This may
  *      require altering the internal representation to fit into that range
@@ -213,8 +299,7 @@ class Number
     using rep = std::int64_t;
     using internalrep = MantissaRange::rep;
 
-    bool negative_{false};
-    internalrep mantissa_{0};
+    rep mantissa_{0};
     int exponent_{std::numeric_limits<int>::lowest()};
 
 public:
@@ -222,9 +307,11 @@ class Number
     constexpr static int minExponent = -32768;
     constexpr static int maxExponent = 32768;
 
+#if MAXREP
     constexpr static internalrep maxRep = std::numeric_limits<rep>::max();
     static_assert(maxRep == 9'223'372'036'854'775'807);
     static_assert(-maxRep == std::numeric_limits<rep>::min() + 1);
+#endif
 
     // May need to make unchecked private
     struct unchecked
@@ -269,6 +356,26 @@ class Number
     constexpr int
     exponent() const noexcept;
 
+    /** Get the scale of this Number for the given asset.
+     *
+     * "scale" is similar to "exponent", but from the perspective of STAmount,
+     * which has different rules for determining the exponent than Number.
+     *
+     * Because Number does not have access to STAmount or Asset, this function
+     * is implemented as a template, with the expectation that it will only be
+     * used by those types. Any types that fit the requirements will work,
+     * though, if there's a need.
+     *
+     * @tparam STAmount The STAmount type.
+     * @tparam Asset The Asset type.
+     * @param asset The asset to use for determining the scale.
+     * @return The scale of this Number for the given asset.
+     */
+    template <class STAmount, class Asset>
+    int
+    scale(Asset const& asset) const
+        requires CanUseAsScale<STAmount, Asset>;
+
     constexpr Number
     operator+() const noexcept;
     constexpr Number
@@ -310,8 +417,7 @@ class Number
     friend constexpr bool
     operator==(Number const& x, Number const& y) noexcept
     {
-        return x.negative_ == y.negative_ && x.mantissa_ == y.mantissa_ &&
-            x.exponent_ == y.exponent_;
+        return x.mantissa_ == y.mantissa_ && x.exponent_ == y.exponent_;
     }
 
     friend constexpr bool
@@ -325,8 +431,8 @@ class Number
     {
         // If the two amounts have different signs (zero is treated as positive)
         // then the comparison is true iff the left is negative.
-        bool const lneg = x.negative_;
-        bool const rneg = y.negative_;
+        bool const lneg = x.mantissa_ < 0;
+        bool const rneg = y.mantissa_ < 0;
 
         if (lneg != rneg)
             return lneg;
@@ -354,7 +460,7 @@ class Number
     constexpr int
     signum() const noexcept
     {
-        return negative_ ? -1 : (mantissa_ ? 1 : 0);
+        return mantissa_ < 0 ? -1 : (mantissa_ ? 1 : 0);
     }
 
     Number
@@ -393,6 +499,9 @@ class Number
     friend Number
     root2(Number f);
 
+    friend Number
+    power(Number const& f, unsigned n, unsigned d);
+
     // Thread local rounding control.  Default is to_nearest
     enum rounding_mode { to_nearest, towards_zero, downward, upward };
     static rounding_mode
@@ -457,22 +566,48 @@ class Number
     static_assert(isPowerOfTen(smallRange.min));
     static_assert(smallRange.min == 1'000'000'000'000'000LL);
     static_assert(smallRange.max == 9'999'999'999'999'999LL);
+    static_assert(smallRange.referenceMin == smallRange.min);
     static_assert(smallRange.log == 15);
+#if MAXREP
     static_assert(smallRange.min < maxRep);
     static_assert(smallRange.max < maxRep);
+#endif
     constexpr static MantissaRange largeRange{MantissaRange::large};
-    static_assert(isPowerOfTen(largeRange.min));
-    static_assert(largeRange.min == 1'000'000'000'000'000'000ULL);
-    static_assert(largeRange.max == internalrep(9'999'999'999'999'999'999ULL));
+    static_assert(!isPowerOfTen(largeRange.min));
+    static_assert(largeRange.min == 922'337'203'685'477'581ULL);
+    static_assert(largeRange.max == internalrep(9'223'372'036'854'775'807ULL));
+    static_assert(largeRange.max == std::numeric_limits<rep>::max());
+    static_assert(largeRange.referenceMin == 1'000'000'000'000'000'000ULL);
     static_assert(largeRange.log == 18);
+    // There are 2 values that will not fit in largeRange without some extra
+    // work
+    // * 9223372036854775808
+    // * 9223372036854775809
+    // They both end up < min, but with a leftover. If they round up, everything
+    // will be fine. If they don't, well need to bring them up into range.
+    // Guard::bringIntoRange handles this situation.
+
+#if MAXREP
     static_assert(largeRange.min < maxRep);
     static_assert(largeRange.max > maxRep);
+#endif
 
     // The range for the mantissa when normalized.
     // Use reference_wrapper to avoid making copies, and prevent accidentally
     // changing the values inside the range.
     static thread_local std::reference_wrapper<MantissaRange const> range_;
 
+    // And one is needed because it needs to choose between oneSmall and
+    // oneLarge based on the current range
+    static Number
+    one(MantissaRange const& range);
+
+    static Number
+    root(MantissaRange const& range, Number f, unsigned d);
+
+    void
+    normalize(MantissaRange const& range);
+
     void
     normalize();
 
@@ -495,11 +630,14 @@ class Number
     friend void
     doNormalize(
         bool& negative,
-        T& mantissa_,
-        int& exponent_,
+        T& mantissa,
+        int& exponent,
         MantissaRange::rep const& minMantissa,
         MantissaRange::rep const& maxMantissa);
 
+    bool
+    isnormal(MantissaRange const& range) const noexcept;
+
     bool
     isnormal() const noexcept;
 
@@ -516,7 +654,64 @@ class Number
     static internalrep
     externalToInternal(rep mantissa);
 
+    /** Breaks down the number into components, potentially de-normalizing it.
+     *
+     * Ensures that the mantissa always has range_.log + 1 digits.
+     *
+     */
+    template <detail::UnsignedMantissa Rep = internalrep>
+    std::tuple<bool, Rep, int>
+    toInternal(MantissaRange const& range) const;
+
+    /** Breaks down the number into components, potentially de-normalizing it.
+     *
+     * Ensures that the mantissa always has range_.log + 1 digits.
+     *
+     */
+    template <detail::UnsignedMantissa Rep = internalrep>
+    std::tuple<bool, Rep, int>
+    toInternal() const;
+
+    /** Rebuilds the number from components.
+     *
+     * If "normalized" is true, the values are expected to be normalized - all
+     * in their valid ranges.
+     *
+     * If "normalized" is false, the values are expected to be "near
+     * normalized", meaning that the mantissa has to be modified at most once to
+     * bring it back into range.
+     *
+     */
+    template <
+        bool expectNormal = true,
+        detail::UnsignedMantissa Rep = internalrep>
+    void
+    fromInternal(
+        bool negative,
+        Rep mantissa,
+        int exponent,
+        MantissaRange const* pRange);
+
+    /** Rebuilds the number from components.
+     *
+     * If "normalized" is true, the values are expected to be normalized - all
+     * in their valid ranges.
+     *
+     * If "normalized" is false, the values are expected to be "near
+     * normalized", meaning that the mantissa has to be modified at most once to
+     * bring it back into range.
+     *
+     */
+    template <
+        bool expectNormal = true,
+        detail::UnsignedMantissa Rep = internalrep>
+    void
+    fromInternal(bool negative, Rep mantissa, int exponent);
+
     class Guard;
+
+public:
+    constexpr static internalrep largestMantissa = largeRange.max;
 };
 
 inline constexpr Number::Number(
@@ -524,7 +719,8 @@ inline constexpr Number::Number(
     internalrep mantissa,
     int exponent,
     unchecked) noexcept
-    : negative_(negative), mantissa_{mantissa}, exponent_{exponent}
+    : mantissa_{(negative ? -1 : 1) * static_cast<rep>(mantissa)}
+    , exponent_{exponent}
 {
 }
 
@@ -538,16 +734,6 @@ inline constexpr Number::Number(
 
 constexpr static Number numZero{};
 
-inline Number::Number(
-    bool negative,
-    internalrep mantissa,
-    int exponent,
-    normalized)
-    : Number(negative, mantissa, exponent, unchecked{})
-{
-    normalize();
-}
-
 inline Number::Number(internalrep mantissa, int exponent, normalized)
     : Number(false, mantissa, exponent, normalized{})
 {
@@ -570,17 +756,7 @@ inline Number::Number(rep mantissa) : Number{mantissa, 0}
 inline constexpr Number::rep
 Number::mantissa() const noexcept
 {
-    auto m = mantissa_;
-    if (m > maxRep)
-    {
-        XRPL_ASSERT_PARTS(
-            !isnormal() || (m % 10 == 0 && m / 10 <= maxRep),
-            "xrpl::Number::mantissa",
-            "large normalized mantissa has no remainder");
-        m /= 10;
-    }
-    auto const sign = negative_ ? -1 : 1;
-    return sign * static_cast<Number::rep>(m);
+    return mantissa_;
 }
 
 /** Returns the exponent of the external view of the Number.
@@ -591,16 +767,15 @@ Number::mantissa() const noexcept
 inline constexpr int
 Number::exponent() const noexcept
 {
-    auto e = exponent_;
-    if (mantissa_ > maxRep)
-    {
-        XRPL_ASSERT_PARTS(
-            !isnormal() || (mantissa_ % 10 == 0 && mantissa_ / 10 <= maxRep),
-            "xrpl::Number::exponent",
-            "large normalized mantissa has no remainder");
-        ++e;
-    }
-    return e;
+    return exponent_;
+}
+
+template <class STAmount, class Asset>
+int
+Number::scale(Asset const& asset) const
+    requires CanUseAsScale<STAmount, Asset>
+{
+    return STAmount{asset, *this}.exponent();
 }
 
 inline constexpr Number
@@ -615,7 +790,7 @@ Number::operator-() const noexcept
     if (mantissa_ == 0)
         return Number{};
     auto x = *this;
-    x.negative_ = !x.negative_;
+    x.mantissa_ = -1 * x.mantissa_;
     return x;
 }
 
@@ -696,45 +871,62 @@ Number::min() noexcept
 inline Number
 Number::max() noexcept
 {
-    return Number{
-        false, std::min(range_.get().max, maxRep), maxExponent, unchecked{}};
+    return Number{false, range_.get().max, maxExponent, unchecked{}};
 }
 
 inline Number
 Number::lowest() noexcept
 {
-    return Number{
-        true, std::min(range_.get().max, maxRep), maxExponent, unchecked{}};
+    return Number{true, range_.get().max, maxExponent, unchecked{}};
 }
 
 inline bool
-Number::isnormal() const noexcept
+Number::isnormal(MantissaRange const& range) const noexcept
 {
-    MantissaRange const& range = range_;
-    auto const abs_m = mantissa_;
+    auto const abs_m = mantissa_ < 0 ? -mantissa_ : mantissa_;
+
     return *this == Number{} ||
-        (range.min <= abs_m && abs_m <= range.max &&
-         (abs_m <= maxRep || abs_m % 10 == 0) && minExponent <= exponent_ &&
-         exponent_ <= maxExponent);
+        (range.min <= abs_m && abs_m <= range.max &&  //
+         minExponent <= exponent_ && exponent_ <= maxExponent);
+}
+
+inline bool
+Number::isnormal() const noexcept
+{
+    return isnormal(range_);
 }
 
 template <Integral64 T>
 std::pair<T, int>
 Number::normalizeToRange(T minMantissa, T maxMantissa) const
 {
-    bool negative = negative_;
-    internalrep mantissa = mantissa_;
+    bool negative = mantissa_ < 0;
+    auto const sign = negative ? -1 : 1;
+    internalrep mantissa = sign * mantissa_;
     int exponent = exponent_;
 
     if constexpr (std::is_unsigned_v<T>)
+    {
         XRPL_ASSERT_PARTS(
             !negative,
             "xrpl::Number::normalizeToRange",
             "Number is non-negative for unsigned range.");
+        // To avoid logical errors in release builds, throw if the Number is
+        // negative for an unsigned range.
+        if (negative)
+            throw std::runtime_error(
+                "Number::normalizeToRange: Number is negative for "
+                "unsigned range.");
+    }
     Number::normalize(negative, mantissa, exponent, minMantissa, maxMantissa);
 
-    auto const sign = negative ? -1 : 1;
-    return std::make_pair(static_cast<T>(sign * mantissa), exponent);
+    // Cast mantissa to signed type first (if T is a signed type) to avoid
+    // unsigned integer overflow when multiplying by negative sign
+    T signedMantissa = static_cast<T>(mantissa);
+    if (negative)
+        signedMantissa = -signedMantissa;
+    return std::make_pair(signedMantissa, exponent);
+    return std::make_pair(sign * static_cast<T>(mantissa), exponent);
 }
 
 inline constexpr Number
diff --git a/include/xrpl/protocol/Protocol.h b/include/xrpl/protocol/Protocol.h
index 43be9d3b45c..30065b38bfa 100644
--- a/include/xrpl/protocol/Protocol.h
+++ b/include/xrpl/protocol/Protocol.h
@@ -233,7 +233,7 @@ std::size_t constexpr maxMPTokenMetadataLength = 1024;
 
 /** The maximum amount of MPTokenIssuance */
 std::uint64_t constexpr maxMPTokenAmount = 0x7FFF'FFFF'FFFF'FFFFull;
-static_assert(Number::maxRep >= maxMPTokenAmount);
+static_assert(Number::largestMantissa >= maxMPTokenAmount);
 
 /** The maximum length of Data payload */
 std::size_t constexpr maxDataPayloadLength = 256;
diff --git a/include/xrpl/protocol/STAmount.h b/include/xrpl/protocol/STAmount.h
index 4d86aed2eca..0c86bc5747a 100644
--- a/include/xrpl/protocol/STAmount.h
+++ b/include/xrpl/protocol/STAmount.h
@@ -568,6 +568,10 @@ STAmount::fromNumber(A const& a, Number const& number)
         return STAmount{asset, intValue, 0, negative};
     }
 
+    XRPL_ASSERT_PARTS(
+        working.signum() >= 0,
+        "ripple::STAmount::fromNumber",
+        "non-negative Number to normalize");
     auto const [mantissa, exponent] =
         working.normalizeToRange(cMinValue, cMaxValue);
 
diff --git a/include/xrpl/protocol/SystemParameters.h b/include/xrpl/protocol/SystemParameters.h
index c2f66e9ea11..fe81ca9bbd8 100644
--- a/include/xrpl/protocol/SystemParameters.h
+++ b/include/xrpl/protocol/SystemParameters.h
@@ -24,7 +24,7 @@ systemName()
 /** Number of drops in the genesis account. */
 constexpr XRPAmount INITIAL_XRP{100'000'000'000 * DROPS_PER_XRP};
 static_assert(INITIAL_XRP.drops() == 100'000'000'000'000'000);
-static_assert(Number::maxRep >= INITIAL_XRP.drops());
+static_assert(Number::largestMantissa >= INITIAL_XRP.drops());
 
 /** Returns true if the amount does not exceed the initial XRP in existence. */
 inline bool
diff --git a/src/libxrpl/basics/Number.cpp b/src/libxrpl/basics/Number.cpp
index 436ebf67790..5a1d84c8d3b 100644
--- a/src/libxrpl/basics/Number.cpp
+++ b/src/libxrpl/basics/Number.cpp
@@ -11,18 +11,16 @@
 #include <numeric>
 #include <stdexcept>
 #include <string>
+#include <string_view>
 #include <type_traits>
 #include <utility>
 
 #ifdef _MSC_VER
 #pragma message("Using boost::multiprecision::uint128_t and int128_t")
-#include <boost/multiprecision/cpp_int.hpp>
-using uint128_t = boost::multiprecision::uint128_t;
-using int128_t = boost::multiprecision::int128_t;
-#else   // !defined(_MSC_VER)
-using uint128_t = __uint128_t;
-using int128_t = __int128_t;
-#endif  // !defined(_MSC_VER)
+#endif
+
+using uint128_t = ripple::detail::uint128_t;
+using int128_t = ripple::detail::int128_t;
 
 namespace xrpl {
 
@@ -62,10 +60,6 @@ Number::setMantissaScale(MantissaRange::mantissa_scale scale)
 // precision to an operation.  This enables the final result
 // to be correctly rounded to the internal precision of Number.
 
-template <class T>
-concept UnsignedMantissa =
-    std::is_unsigned_v<T> || std::is_same_v<T, uint128_t>;
-
 class Number::Guard
 {
     std::uint64_t digits_;   // 16 decimal guard digits
@@ -101,7 +95,7 @@ class Number::Guard
     round() noexcept;
 
     // Modify the result to the correctly rounded value
-    template <UnsignedMantissa T>
+    template <detail::UnsignedMantissa T>
     void
     doRoundUp(
         bool& negative,
@@ -109,10 +103,10 @@ class Number::Guard
         int& exponent,
         internalrep const& minMantissa,
         internalrep const& maxMantissa,
-        std::string location);
+        std::string_view location);
 
     // Modify the result to the correctly rounded value
-    template <UnsignedMantissa T>
+    template <detail::UnsignedMantissa T>
     void
     doRoundDown(
         bool& negative,
@@ -122,13 +116,13 @@ class Number::Guard
 
     // Modify the result to the correctly rounded value
     void
-    doRound(rep& drops, std::string location);
+    doRound(rep& drops, std::string_view location);
 
 private:
     void
     doPush(unsigned d) noexcept;
 
-    template <UnsignedMantissa T>
+    template <detail::UnsignedMantissa T>
     void
     bringIntoRange(
         bool& negative,
@@ -219,7 +213,7 @@ Number::Guard::round() noexcept
     return 0;
 }
 
-template <UnsignedMantissa T>
+template <detail::UnsignedMantissa T>
 void
 Number::Guard::bringIntoRange(
     bool& negative,
@@ -238,13 +232,13 @@ Number::Guard::bringIntoRange(
     {
         constexpr Number zero = Number{};
 
-        negative = zero.negative_;
+        negative = false;
         mantissa = zero.mantissa_;
         exponent = zero.exponent_;
     }
 }
 
-template <UnsignedMantissa T>
+template <detail::UnsignedMantissa T>
 void
 Number::Guard::doRoundUp(
     bool& negative,
@@ -252,7 +246,7 @@ Number::Guard::doRoundUp(
     int& exponent,
     internalrep const& minMantissa,
     internalrep const& maxMantissa,
-    std::string location)
+    std::string_view location)
 {
     auto r = round();
     if (r == 1 || (r == 0 && (mantissa & 1) == 1))
@@ -260,7 +254,7 @@ Number::Guard::doRoundUp(
         ++mantissa;
         // Ensure mantissa after incrementing fits within both the
         // min/maxMantissa range and is a valid "rep".
-        if (mantissa > maxMantissa || mantissa > maxRep)
+        if (mantissa > maxMantissa)
         {
             mantissa /= 10;
             ++exponent;
@@ -268,10 +262,10 @@ Number::Guard::doRoundUp(
     }
     bringIntoRange(negative, mantissa, exponent, minMantissa);
     if (exponent > maxExponent)
-        throw std::overflow_error(location);
+        throw std::overflow_error(std::string{location});
 }
 
-template <UnsignedMantissa T>
+template <detail::UnsignedMantissa T>
 void
 Number::Guard::doRoundDown(
     bool& negative,
@@ -294,12 +288,13 @@ Number::Guard::doRoundDown(
 
 // Modify the result to the correctly rounded value
 void
-Number::Guard::doRound(rep& drops, std::string location)
+Number::Guard::doRound(rep& drops, std::string_view location)
 {
     auto r = round();
     if (r == 1 || (r == 0 && (drops & 1) == 1))
     {
-        if (drops >= maxRep)
+        auto const& range = range_.get();
+        if (drops >= range.max)
         {
             static_assert(sizeof(internalrep) == sizeof(rep));
             // This should be impossible, because it's impossible to represent
@@ -308,7 +303,7 @@ Number::Guard::doRound(rep& drops, std::string location)
             // or "(maxRep + 1) / 10", neither of which will round up when
             // converting to rep, though the latter might overflow _before_
             // rounding.
-            throw std::overflow_error(location);  // LCOV_EXCL_LINE
+            throw std::overflow_error(std::string{location});  // LCOV_EXCL_LINE
         }
         ++drops;
     }
@@ -328,17 +323,134 @@ Number::externalToInternal(rep mantissa)
     // If the mantissa is already positive, just return it
     if (mantissa >= 0)
         return mantissa;
-    // If the mantissa is negative, but fits within the positive range of rep,
-    // return it negated
-    if (mantissa >= -std::numeric_limits<rep>::max())
-        return -mantissa;
-
-    // If the mantissa doesn't fit within the positive range, convert to
-    // int128_t, negate that, and cast it back down to the internalrep
-    // In practice, this is only going to cover the case of
-    // std::numeric_limits<rep>::min().
-    int128_t temp = mantissa;
-    return static_cast<internalrep>(-temp);
+
+    // Cast to unsigned before negating to avoid undefined behavior
+    // when v == INT64_MIN (negating INT64_MIN in signed is UB)
+    return -static_cast<internalrep>(mantissa);
+}
+
+/** Breaks down the number into components, potentially de-normalizing it.
+ *
+ * Ensures that the mantissa always has range_.log digits.
+ *
+ */
+template <detail::UnsignedMantissa Rep>
+std::tuple<bool, Rep, int>
+Number::toInternal(MantissaRange const& range) const
+{
+    auto exponent = exponent_;
+    bool const negative = mantissa_ < 0;
+    auto const sign = negative ? -1 : 1;
+    Rep mantissa = static_cast<Rep>(sign * mantissa_);
+
+    auto const referenceMin = range.referenceMin;
+    auto const minMantissa = range.min;
+
+    if (mantissa != 0 && mantissa >= minMantissa && mantissa < referenceMin)
+    {
+        // Ensure the mantissa has the correct number of digits
+        mantissa *= 10;
+        --exponent;
+        XRPL_ASSERT_PARTS(
+            mantissa >= referenceMin && mantissa < referenceMin * 10,
+            "ripple::Number::toInternal()",
+            "Number is within reference range and has 'log' digits");
+    }
+
+    return {negative, mantissa, exponent};
+}
+
+/** Breaks down the number into components, potentially de-normalizing it.
+ *
+ * Ensures that the mantissa always has range_.log digits.
+ *
+ */
+template <detail::UnsignedMantissa Rep>
+std::tuple<bool, Rep, int>
+Number::toInternal() const
+{
+    return toInternal(range_);
+}
+
+/** Rebuilds the number from components.
+ *
+ * If "normalized" is true, the values are expected to be normalized - all
+ * in their valid ranges.
+ *
+ * If "normalized" is false, the values are expected to be "near
+ * normalized", meaning that the mantissa has to be modified at most once to
+ * bring it back into range.
+ *
+ */
+template <bool expectNormal, detail::UnsignedMantissa Rep>
+void
+Number::fromInternal(
+    bool negative,
+    Rep mantissa,
+    int exponent,
+    MantissaRange const* pRange)
+{
+    if constexpr (std::is_same_v<
+                      std::bool_constant<expectNormal>,
+                      std::false_type>)
+    {
+        if (!pRange)
+            throw std::runtime_error("Missing range to Number::fromInternal!");
+        auto const& range = *pRange;
+
+        auto const maxMantissa = range.max;
+        auto const minMantissa = range.min;
+
+        XRPL_ASSERT_PARTS(
+            mantissa >= minMantissa,
+            "ripple::Number::fromInternal",
+            "mantissa large enough");
+
+        if (mantissa > maxMantissa || mantissa < minMantissa)
+        {
+            normalize(negative, mantissa, exponent, range.min, maxMantissa);
+        }
+
+        XRPL_ASSERT_PARTS(
+            mantissa >= minMantissa && mantissa <= maxMantissa,
+            "ripple::Number::fromInternal",
+            "mantissa in range");
+    }
+
+    auto const sign = negative ? -1 : 1;
+
+    mantissa_ = sign * static_cast<rep>(mantissa);
+    exponent_ = exponent;
+
+    XRPL_ASSERT_PARTS(
+        (pRange && isnormal(*pRange)) || isnormal(),
+        "ripple::Number::fromInternal",
+        "Number is normalized");
+}
+
+/** Rebuilds the number from components.
+ *
+ * If "normalized" is true, the values are expected to be normalized - all in
+ * their valid ranges.
+ *
+ * If "normalized" is false, the values are expected to be "near normalized",
+ * meaning that the mantissa has to be modified at most once to bring it back
+ * into range.
+ *
+ */
+template <bool expectNormal, detail::UnsignedMantissa Rep>
+void
+Number::fromInternal(bool negative, Rep mantissa, int exponent)
+{
+    MantissaRange const* pRange = nullptr;
+    if constexpr (std::is_same_v<
+                      std::bool_constant<expectNormal>,
+                      std::false_type>)
+    {
+        pRange = &Number::range_.get();
+    }
+
+    fromInternal(negative, mantissa, exponent, pRange);
 }
 
 constexpr Number
@@ -346,7 +458,7 @@ Number::oneSmall()
 {
     return Number{
         false,
-        Number::smallRange.min,
+        Number::smallRange.referenceMin,
         -Number::smallRange.log,
         Number::unchecked{}};
 };
@@ -358,7 +470,7 @@ Number::oneLarge()
 {
     return Number{
         false,
-        Number::largeRange.min,
+        Number::largeRange.referenceMin,
         -Number::largeRange.log,
         Number::unchecked{}};
 };
@@ -366,106 +478,91 @@ Number::oneLarge()
 constexpr Number oneLrg = Number::oneLarge();
 
 Number
-Number::one()
+Number::one(MantissaRange const& range)
 {
-    if (&range_.get() == &smallRange)
+    if (&range == &smallRange)
         return oneSml;
-    XRPL_ASSERT(&range_.get() == &largeRange, "Number::one() : valid range_");
+    XRPL_ASSERT(&range == &largeRange, "Number::one() : valid range");
     return oneLrg;
 }
 
+Number
+Number::one()
+{
+    return one(range_);
+}
+
 // Use the member names in this static function for now so the diff is cleaner
-// TODO: Rename the function parameters to get rid of the "_" suffix
 template <class T>
 void
 doNormalize(
     bool& negative,
-    T& mantissa_,
-    int& exponent_,
+    T& mantissa,
+    int& exponent,
     MantissaRange::rep const& minMantissa,
     MantissaRange::rep const& maxMantissa)
 {
     auto constexpr minExponent = Number::minExponent;
     auto constexpr maxExponent = Number::maxExponent;
-    auto constexpr maxRep = Number::maxRep;
 
     using Guard = Number::Guard;
 
     constexpr Number zero = Number{};
-    if (mantissa_ == 0)
+    if (mantissa == 0 || (mantissa < minMantissa && exponent <= minExponent))
     {
-        mantissa_ = zero.mantissa_;
-        exponent_ = zero.exponent_;
-        negative = zero.negative_;
+        mantissa = zero.mantissa_;
+        exponent = zero.exponent_;
+        negative = false;
         return;
     }
-    auto m = mantissa_;
-    while ((m < minMantissa) && (exponent_ > minExponent))
+
+    auto m = mantissa;
+    while ((m < minMantissa) && (exponent > minExponent))
     {
         m *= 10;
-        --exponent_;
+        --exponent;
     }
     Guard g;
     if (negative)
         g.set_negative();
     while (m > maxMantissa)
     {
-        if (exponent_ >= maxExponent)
+        if (exponent >= maxExponent)
             throw std::overflow_error("Number::normalize 1");
         g.push(m % 10);
         m /= 10;
-        ++exponent_;
+        ++exponent;
     }
-    if ((exponent_ < minExponent) || (m < minMantissa))
+    if ((exponent < minExponent) || (m == 0))
     {
-        mantissa_ = zero.mantissa_;
-        exponent_ = zero.exponent_;
-        negative = zero.negative_;
+        mantissa = zero.mantissa_;
+        exponent = zero.exponent_;
+        negative = false;
         return;
     }
 
-    // When using the largeRange, "m" needs fit within an int64, even if
-    // the final mantissa_ is going to end up larger to fit within the
-    // MantissaRange. Cut it down here so that the rounding will be done while
-    // it's smaller.
-    //
-    // Example: 9,900,000,000,000,123,456 > 9,223,372,036,854,775,807,
-    //      so "m" will be modified to 990,000,000,000,012,345. Then that value
-    //      will be rounded to 990,000,000,000,012,345 or
-    //      990,000,000,000,012,346, depending on the rounding mode. Finally,
-    //      mantissa_ will be "m*10" so it fits within the range, and end up as
-    //      9,900,000,000,000,123,450 or 9,900,000,000,000,123,460.
-    // mantissa() will return mantissa_ / 10, and exponent() will return
-    // exponent_ + 1.
-    if (m > maxRep)
-    {
-        if (exponent_ >= maxExponent)
-            throw std::overflow_error("Number::normalize 1.5");
-        g.push(m % 10);
-        m /= 10;
-        ++exponent_;
-    }
-    // Before modification, m should be within the min/max range. After
-    // modification, it must be less than maxRep. In other words, the original
-    // value should have been no more than maxRep * 10.
-    // (maxRep * 10 > maxMantissa)
     XRPL_ASSERT_PARTS(
-        m <= maxRep,
+        m <= maxMantissa,
         "xrpl::doNormalize",
         "intermediate mantissa fits in int64");
-    mantissa_ = m;
+    mantissa = m;
 
     g.doRoundUp(
         negative,
-        mantissa_,
-        exponent_,
+        mantissa,
+        exponent,
         minMantissa,
         maxMantissa,
         "Number::normalize 2");
+
     XRPL_ASSERT_PARTS(
-        mantissa_ >= minMantissa && mantissa_ <= maxMantissa,
+        mantissa >= minMantissa && mantissa <= maxMantissa,
         "xrpl::doNormalize",
         "final mantissa fits in range");
+    XRPL_ASSERT_PARTS(
+        exponent >= minExponent && exponent <= maxExponent,
+        "xrpl::doNormalize",
+        "final exponent fits in range");
 }
 
 template <>
@@ -504,11 +601,20 @@ Number::normalize<unsigned long>(
     doNormalize(negative, mantissa, exponent, minMantissa, maxMantissa);
 }
 
+void
+Number::normalize(MantissaRange const& range)
+{
+    auto [negative, mantissa, exponent] = toInternal(range);
+
+    normalize(negative, mantissa, exponent, range.min, range.max);
+
+    fromInternal(negative, mantissa, exponent, &range);
+}
+
 void
 Number::normalize()
 {
-    auto const& range = range_.get();
-    normalize(negative_, mantissa_, exponent_, range.min, range.max);
+    normalize(range_);
 }
 
 // Copy the number, but set a new exponent. Because the mantissa doesn't change,
@@ -518,24 +624,33 @@ Number
 Number::shiftExponent(int exponentDelta) const
 {
     XRPL_ASSERT_PARTS(isnormal(), "xrpl::Number::shiftExponent", "normalized");
-    auto const newExponent = exponent_ + exponentDelta;
-    if (newExponent >= maxExponent)
+
+    Number result = *this;
+
+    result.exponent_ += exponentDelta;
+
+    if (result.exponent_ >= maxExponent)
         throw std::overflow_error("Number::shiftExponent");
-    if (newExponent < minExponent)
+    if (result.exponent_ < minExponent)
     {
         return Number{};
     }
-    Number const result{negative_, mantissa_, newExponent, unchecked{}};
-    XRPL_ASSERT_PARTS(
-        result.isnormal(),
-        "xrpl::Number::shiftExponent",
-        "result is normalized");
+
     return result;
 }
 
+Number::Number(bool negative, internalrep mantissa, int exponent, normalized)
+{
+    auto const& range = range_.get();
+    normalize(negative, mantissa, exponent, range.min, range.max);
+    fromInternal(negative, mantissa, exponent, &range);
+}
+
 Number&
 Number::operator+=(Number const& y)
 {
+    auto const& range = range_.get();
+
     constexpr Number zero = Number{};
     if (y == zero)
         return *this;
@@ -551,7 +666,7 @@ Number::operator+=(Number const& y)
     }
 
     XRPL_ASSERT(
-        isnormal() && y.isnormal(),
+        isnormal(range) && y.isnormal(range),
         "xrpl::Number::operator+=(Number) : is normal");
     // *n = negative
     // *s = sign
@@ -560,13 +675,10 @@ Number::operator+=(Number const& y)
 
     // Need to use uint128_t, because large mantissas can overflow when added
     // together.
-    bool xn = negative_;
-    uint128_t xm = mantissa_;
-    auto xe = exponent_;
+    auto [xn, xm, xe] = toInternal<uint128_t>(range);
+
+    auto [yn, ym, ye] = y.toInternal<uint128_t>(range);
 
-    bool yn = y.negative_;
-    uint128_t ym = y.mantissa_;
-    auto ye = y.exponent_;
     Guard g;
     if (xe < ye)
     {
@@ -591,14 +703,13 @@ Number::operator+=(Number const& y)
         } while (xe > ye);
     }
 
-    auto const& range = range_.get();
     auto const& minMantissa = range.min;
     auto const& maxMantissa = range.max;
 
     if (xn == yn)
     {
         xm += ym;
-        if (xm > maxMantissa || xm > maxRep)
+        if (xm > maxMantissa)
         {
             g.push(xm % 10);
             xm /= 10;
@@ -619,7 +730,7 @@ Number::operator+=(Number const& y)
             xe = ye;
             xn = yn;
         }
-        while (xm < minMantissa && xm * 10 <= maxRep)
+        while (xm < minMantissa)
         {
             xm *= 10;
             xm -= g.pop();
@@ -628,10 +739,8 @@ Number::operator+=(Number const& y)
         g.doRoundDown(xn, xm, xe, minMantissa);
     }
 
-    negative_ = xn;
-    mantissa_ = static_cast<internalrep>(xm);
-    exponent_ = xe;
-    normalize();
+    normalize(xn, xm, xe, minMantissa, maxMantissa);
+    fromInternal(xn, xm, xe, &range);
     return *this;
 }
 
@@ -666,6 +775,8 @@ divu10(uint128_t& u)
 Number&
 Number::operator*=(Number const& y)
 {
+    auto const& range = range_.get();
+
     constexpr Number zero = Number{};
     if (*this == zero)
         return *this;
@@ -679,15 +790,11 @@ Number::operator*=(Number const& y)
     // *m = mantissa
     // *e = exponent
 
-    bool xn = negative_;
+    auto [xn, xm, xe] = toInternal(range);
     int xs = xn ? -1 : 1;
-    internalrep xm = mantissa_;
-    auto xe = exponent_;
 
-    bool yn = y.negative_;
+    auto [yn, ym, ye] = y.toInternal(range);
     int ys = yn ? -1 : 1;
-    internalrep ym = y.mantissa_;
-    auto ye = y.exponent_;
 
     auto zm = uint128_t(xm) * uint128_t(ym);
     auto ze = xe + ye;
@@ -697,11 +804,10 @@ Number::operator*=(Number const& y)
     if (zn)
         g.set_negative();
 
-    auto const& range = range_.get();
     auto const& minMantissa = range.min;
     auto const& maxMantissa = range.max;
 
-    while (zm > maxMantissa || zm > maxRep)
+    while (zm > maxMantissa)
     {
         // The following is optimization for:
         // g.push(static_cast<unsigned>(zm % 10));
@@ -718,17 +824,17 @@ Number::operator*=(Number const& y)
         minMantissa,
         maxMantissa,
         "Number::multiplication overflow : exponent is " + std::to_string(xe));
-    negative_ = zn;
-    mantissa_ = xm;
-    exponent_ = xe;
 
-    normalize();
+    normalize(zn, xm, xe, minMantissa, maxMantissa);
+    fromInternal(zn, xm, xe, &range);
     return *this;
 }
 
 Number&
 Number::operator/=(Number const& y)
 {
+    auto const& range = range_.get();
+
     constexpr Number zero = Number{};
     if (y == zero)
         throw std::overflow_error("Number: divide by 0");
@@ -741,17 +847,12 @@ Number::operator/=(Number const& y)
     // *m = mantissa
     // *e = exponent
 
-    bool np = negative_;
+    auto [np, nm, ne] = toInternal(range);
     int ns = (np ? -1 : 1);
-    auto nm = mantissa_;
-    auto ne = exponent_;
 
-    bool dp = y.negative_;
+    auto [dp, dm, de] = y.toInternal(range);
     int ds = (dp ? -1 : 1);
-    auto dm = y.mantissa_;
-    auto de = y.exponent_;
 
-    auto const& range = range_.get();
     auto const& minMantissa = range.min;
     auto const& maxMantissa = range.max;
 
@@ -763,7 +864,7 @@ Number::operator/=(Number const& y)
     // f can be up to 10^(38-19) = 10^19 safely
     static_assert(smallRange.log == 15);
     static_assert(largeRange.log == 18);
-    bool small = Number::getMantissaScale() == MantissaRange::small;
+    bool small = range.scale == MantissaRange::small;
     uint128_t const f =
         small ? 100'000'000'000'000'000 : 10'000'000'000'000'000'000ULL;
     XRPL_ASSERT_PARTS(
@@ -815,11 +916,9 @@ Number::operator/=(Number const& y)
         }
     }
     normalize(zn, zm, ze, minMantissa, maxMantissa);
-    negative_ = zn;
-    mantissa_ = static_cast<internalrep>(zm);
-    exponent_ = ze;
+    fromInternal(zn, zm, ze, &range);
     XRPL_ASSERT_PARTS(
-        isnormal(), "xrpl::Number::operator/=", "result is normalized");
+        isnormal(range), "xrpl::Number::operator/=", "result is normalized");
 
     return *this;
 }
@@ -831,7 +930,7 @@ Number::operator rep() const
     Guard g;
     if (drops != 0)
     {
-        if (negative_)
+        if (drops < 0)
         {
             g.set_negative();
             drops = -drops;
@@ -843,7 +942,7 @@ Number::operator rep() const
         }
         for (; offset > 0; --offset)
         {
-            if (drops > maxRep / 10)
+            if (drops >= largeRange.min)
                 throw std::overflow_error("Number::operator rep() overflow");
             drops *= 10;
         }
@@ -873,20 +972,22 @@ Number::truncate() const noexcept
 std::string
 to_string(Number const& amount)
 {
+    auto const& range = Number::range_.get();
+
     // keep full internal accuracy, but make more human friendly if possible
     constexpr Number zero = Number{};
     if (amount == zero)
         return "0";
 
-    auto exponent = amount.exponent_;
-    auto mantissa = amount.mantissa_;
-    bool const negative = amount.negative_;
+    // The mantissa must have a set number of decimal places for this to work
+    auto [negative, mantissa, exponent] = amount.toInternal(range);
 
     // Use scientific notation for exponents that are too small or too large
-    auto const rangeLog = Number::mantissaLog();
-    if (((exponent != 0) &&
+    auto const rangeLog = range.log;
+    if (((exponent != 0 && amount.exponent() != 0) &&
          ((exponent < -(rangeLog + 10)) || (exponent > -(rangeLog - 10)))))
     {
+        // Remove trailing zeroes from the mantissa.
         while (mantissa != 0 && mantissa % 10 == 0 &&
                exponent < Number::maxExponent)
         {
@@ -895,8 +996,11 @@ to_string(Number const& amount)
         }
         std::string ret = negative ? "-" : "";
         ret.append(std::to_string(mantissa));
-        ret.append(1, 'e');
-        ret.append(std::to_string(exponent));
+        if (exponent != 0)
+        {
+            ret.append(1, 'e');
+            ret.append(std::to_string(exponent));
+        }
         return ret;
     }
 
@@ -984,20 +1088,11 @@ power(Number const& f, unsigned n)
     return r;
 }
 
-// Returns f^(1/d)
-// Uses Newton–Raphson iterations until the result stops changing
-// to find the non-negative root of the polynomial g(x) = x^d - f
-
-// This function, and power(Number f, unsigned n, unsigned d)
-// treat corner cases such as 0 roots as advised by Annex F of
-// the C standard, which itself is consistent with the IEEE
-// floating point standards.
-
 Number
-root(Number f, unsigned d)
+Number::root(MantissaRange const& range, Number f, unsigned d)
 {
     constexpr Number zero = Number{};
-    auto const one = Number::one();
+    auto const one = Number::one(range);
 
     if (f == one || d == 1)
         return f;
@@ -1014,22 +1109,30 @@ root(Number f, unsigned d)
     if (f == zero)
         return f;
 
-    // Scale f into the range (0, 1) such that f's exponent is a multiple of d
-    auto e = f.exponent_ + Number::mantissaLog() + 1;
-    auto const di = static_cast<int>(d);
-    auto ex = [e = e, di = di]()  // Euclidean remainder of e/d
-    {
-        int k = (e >= 0 ? e : e - (di - 1)) / di;
-        int k2 = e - k * di;
-        if (k2 == 0)
-            return 0;
-        return di - k2;
+    auto const [e, di] = [&]() {
+        auto const [negative, mantissa, exponent] = f.toInternal(range);
+
+        // Scale f into the range (0, 1) such that the scale change (e) is a
+        // multiple of the root (d)
+        auto e = exponent + range.log + 1;
+        auto const di = static_cast<int>(d);
+        auto ex = [e = e, di = di]()  // Euclidean remainder of e/d
+        {
+            int k = (e >= 0 ? e : e - (di - 1)) / di;
+            int k2 = e - k * di;
+            if (k2 == 0)
+                return 0;
+            return di - k2;
+        }();
+        e += ex;
+        f = f.shiftExponent(-e);  // f /= 10^e;
+        return std::make_tuple(e, di);
     }();
-    e += ex;
-    f = f.shiftExponent(-e);  // f /= 10^e;
 
     XRPL_ASSERT_PARTS(
-        f.isnormal(), "xrpl::root(Number, unsigned)", "f is normalized");
+        e % di == 0, "xrpl::root(Number, unsigned)", "e is divisible by d");
+    XRPL_ASSERT_PARTS(
+        f.isnormal(range), "xrpl::root(Number, unsigned)", "f is normalized");
     bool neg = false;
     if (f < zero)
     {
@@ -1063,17 +1166,34 @@ root(Number f, unsigned d)
     //  return r * 10^(e/d) to reverse scaling
     auto const result = r.shiftExponent(e / di);
     XRPL_ASSERT_PARTS(
-        result.isnormal(),
+        result.isnormal(range),
         "xrpl::root(Number, unsigned)",
         "result is normalized");
     return result;
 }
 
+// Returns f^(1/d)
+// Uses Newton–Raphson iterations until the result stops changing
+// to find the non-negative root of the polynomial g(x) = x^d - f
+
+// This function, and power(Number f, unsigned n, unsigned d)
+// treat corner cases such as 0 roots as advised by Annex F of
+// the C standard, which itself is consistent with the IEEE
+// floating point standards.
+
+Number
+root(Number f, unsigned d)
+{
+    auto const& range = Number::range_.get();
+    return Number::root(range, f, d);
+}
+
 Number
 root2(Number f)
 {
+    auto const& range = Number::range_.get();
     constexpr Number zero = Number{};
-    auto const one = Number::one();
+    auto const one = Number::one(range);
 
     if (f == one)
         return f;
@@ -1082,12 +1202,19 @@ root2(Number f)
     if (f == zero)
         return f;
 
-    // Scale f into the range (0, 1) such that f's exponent is a multiple of d
-    auto e = f.exponent_ + Number::mantissaLog() + 1;
-    if (e % 2 != 0)
-        ++e;
-    f = f.shiftExponent(-e);  // f /= 10^e;
-    XRPL_ASSERT_PARTS(f.isnormal(), "xrpl::root2(Number)", "f is normalized");
+    auto const e = [&]() {
+        auto const [negative, mantissa, exponent] = f.toInternal(range);
+
+        // Scale f into the range (0, 1) such that f's exponent is a
+        // multiple of d
+        auto e = exponent + range.log + 1;
+        if (e % 2 != 0)
+            ++e;
+        f = f.shiftExponent(-e);  // f /= 10^e;
+        return e;
+    }();
+    XRPL_ASSERT_PARTS(
+        f.isnormal(range), "xrpl::root2(Number)", "f is normalized");
 
     // Quadratic least squares curve fit of f^(1/d) in the range [0, 1]
     auto const D = 105;
@@ -1110,7 +1237,7 @@ root2(Number f)
     //  return r * 10^(e/2) to reverse scaling
     auto const result = r.shiftExponent(e / 2);
     XRPL_ASSERT_PARTS(
-        result.isnormal(), "xrpl::root2(Number)", "result is normalized");
+        result.isnormal(range), "xrpl::root2(Number)", "result is normalized");
 
     return result;
 }
@@ -1120,8 +1247,10 @@ root2(Number f)
 Number
 power(Number const& f, unsigned n, unsigned d)
 {
+    auto const& range = Number::range_.get();
+
     constexpr Number zero = Number{};
-    auto const one = Number::one();
+    auto const one = Number::one(range);
 
     if (f == one)
         return f;
@@ -1143,7 +1272,7 @@ power(Number const& f, unsigned n, unsigned d)
     d /= g;
     if ((n % 2) == 1 && (d % 2) == 0 && f < zero)
         throw std::overflow_error("Number::power nan");
-    return root(power(f, n), d);
+    return Number::root(range, power(f, n), d);
 }
 
 }  // namespace xrpl
diff --git a/src/test/app/Invariants_test.cpp b/src/test/app/Invariants_test.cpp
index 1e81959ae65..c7327542b44 100644
--- a/src/test/app/Invariants_test.cpp
+++ b/src/test/app/Invariants_test.cpp
@@ -4,6 +4,7 @@
 
 #include <xrpld/app/tx/apply.h>
 #include <xrpld/app/tx/detail/ApplyContext.h>
+#include <xrpld/app/tx/detail/InvariantCheck.h>
 
 #include <xrpl/beast/unit_test/suite.h>
 #include <xrpl/beast/utility/Journal.h>
@@ -3891,6 +3892,140 @@ class Invariants_test : public beast::unit_test::suite
             precloseMpt);
     }
 
+    void
+    testVaultComputeMinScale()
+    {
+        using namespace jtx;
+
+        Account const issuer{"issuer"};
+        PrettyAsset const vaultAsset = issuer["IOU"];
+
+        struct TestCase
+        {
+            std::string name;
+            std::int32_t expectedMinScale;
+            std::initializer_list<ValidVault::DeltaInfo const> values;
+        };
+
+        NumberMantissaScaleGuard g{MantissaRange::large};
+
+        auto makeDelta =
+            [&vaultAsset](Number const& n) -> ValidVault::DeltaInfo {
+            return {n, n.scale<STAmount>(vaultAsset.raw())};
+        };
+
+        auto const testCases = std::vector<TestCase>{
+            {
+                .name = "No values",
+                .expectedMinScale = 0,
+                .values = {},
+            },
+            {
+                .name = "Mixed integer and Number values",
+                .expectedMinScale = -15,
+                .values =
+                    {makeDelta(1), makeDelta(-1), makeDelta(Number{10, -1})},
+            },
+            {
+                .name = "Mixed scales",
+                .expectedMinScale = -17,
+                .values =
+                    {makeDelta(Number{1, -2}),
+                     makeDelta(Number{5, -3}),
+                     makeDelta(Number{3, -2})},
+            },
+            {
+                .name = "Equal scales",
+                .expectedMinScale = -16,
+                .values =
+                    {makeDelta(Number{1, -1}),
+                     makeDelta(Number{5, -1}),
+                     makeDelta(Number{1, -1})},
+            },
+            {
+                .name = "Mixed mantissa sizes",
+                .expectedMinScale = -12,
+                .values =
+                    {makeDelta(Number{1}),
+                     makeDelta(Number{1234, -3}),
+                     makeDelta(Number{12345, -6}),
+                     makeDelta(Number{123, 1})},
+            },
+        };
+
+        for (auto const& tc : testCases)
+        {
+            testcase("vault computeMinScale: " + tc.name);
+
+            auto const actualScale =
+                ValidVault::computeMinScale(vaultAsset, tc.values);
+
+            BEAST_EXPECTS(
+                actualScale == tc.expectedMinScale,
+                "expected: " + std::to_string(tc.expectedMinScale) +
+                    ", actual: " + std::to_string(actualScale));
+            for (auto const& num : tc.values)
+            {
+                // None of these scales are far enough apart that rounding the
+                // values would lose information, so check that the rounded
+                // value matches the original.
+                auto const actualRounded =
+                    roundToAsset(vaultAsset, num.delta, actualScale);
+                BEAST_EXPECTS(
+                    actualRounded == num.delta,
+                    "number " + to_string(num.delta) + " rounded to scale " +
+                        std::to_string(actualScale) + " is " +
+                        to_string(actualRounded));
+            }
+        }
+
+        auto const testCases2 = std::vector<TestCase>{
+            {
+                .name = "False equivalence",
+                .expectedMinScale = -15,
+                .values =
+                    {
+                        makeDelta(Number{1234567890123456789, -18}),
+                        makeDelta(Number{12345, -4}),
+                        makeDelta(Number{1}),
+                    },
+            },
+        };
+
+        // Unlike the first set of test cases, the values in these test could
+        // look equivalent if using the wrong scale.
+        for (auto const& tc : testCases2)
+        {
+            testcase("vault computeMinScale: " + tc.name);
+
+            auto const actualScale =
+                ValidVault::computeMinScale(vaultAsset, tc.values);
+
+            BEAST_EXPECTS(
+                actualScale == tc.expectedMinScale,
+                "expected: " + std::to_string(tc.expectedMinScale) +
+                    ", actual: " + std::to_string(actualScale));
+            std::optional<Number> first;
+            Number firstRounded;
+            for (auto const& num : tc.values)
+            {
+                if (!first)
+                {
+                    first = num.delta;
+                    firstRounded =
+                        roundToAsset(vaultAsset, num.delta, actualScale);
+                    continue;
+                }
+                auto const numRounded =
+                    roundToAsset(vaultAsset, num.delta, actualScale);
+                BEAST_EXPECTS(
+                    numRounded != firstRounded,
+                    "at a scale of " + std::to_string(actualScale) + " " +
+                        to_string(num.delta) + " == " + to_string(*first));
+            }
+        }
+    }
+
 public:
     void
     run() override
@@ -3914,6 +4049,7 @@ class Invariants_test : public beast::unit_test::suite
         testValidPseudoAccounts();
         testValidLoanBroker();
         testVault();
+        testVaultComputeMinScale();
     }
 };
 
diff --git a/src/test/basics/Number_test.cpp b/src/test/basics/Number_test.cpp
index 1fa5ae6e8fb..4da06214394 100644
--- a/src/test/basics/Number_test.cpp
+++ b/src/test/basics/Number_test.cpp
@@ -32,9 +32,10 @@ class Number_test : public beast::unit_test::suite
     test_limits()
     {
         auto const scale = Number::getMantissaScale();
-        testcase << "test_limits " << to_string(scale);
-        bool caught = false;
         auto const minMantissa = Number::minMantissa();
+
+        testcase << "test_limits " << to_string(scale) << ", " << minMantissa;
+        bool caught = false;
         try
         {
             Number x =
@@ -62,8 +63,9 @@ class Number_test : public beast::unit_test::suite
             Number{},
             __LINE__);
         test(
+            // Use 1501 to force rounding up
             Number{false, minMantissa, 32000, Number::normalized{}} * 1'000 +
-                Number{false, 1'500, 32000, Number::normalized{}},
+                Number{false, 1'501, 32000, Number::normalized{}},
             Number{false, minMantissa + 2, 32003, Number::normalized{}},
             __LINE__);
         // 9,223,372,036,854,775,808
@@ -198,12 +200,12 @@ class Number_test : public beast::unit_test::suite
                      9'999'999'999'999'999'990ULL,
                      -19,
                      Number::normalized{}}},
-                {Number{Number::maxRep},
+                {Number{Number::largestMantissa},
                  Number{6, -1},
-                 Number{Number::maxRep / 10, 1}},
-                {Number{Number::maxRep - 1},
+                 Number{Number::largestMantissa / 10, 1}},
+                {Number{Number::largestMantissa - 1},
                  Number{1, 0},
-                 Number{Number::maxRep}},
+                 Number{Number::largestMantissa}},
                 // Test extremes
                 {
                     // Each Number operand rounds up, so the actual mantissa is
@@ -221,11 +223,30 @@ class Number_test : public beast::unit_test::suite
                     Number{2, 19},
                 },
                 {
-                    // Does not round. Mantissas are going to be > maxRep, so if
-                    // added together as uint64_t's, the result will overflow.
-                    // With addition using uint128_t, there's no problem. After
-                    // normalizing, the resulting mantissa ends up less than
-                    // maxRep.
+                    // Does not round. Mantissas are going to be >
+                    // largestMantissa, so if added together as uint64_t's, the
+                    // result will overflow. With addition using uint128_t,
+                    // there's no problem. After normalizing, the resulting
+                    // mantissa ends up less than largestMantissa.
+                    Number{
+                        false,
+                        Number::largestMantissa,
+                        0,
+                        Number::normalized{}},
+                    Number{
+                        false,
+                        Number::largestMantissa,
+                        0,
+                        Number::normalized{}},
+                    Number{
+                        false,
+                        Number::largestMantissa * 2,
+                        0,
+                        Number::normalized{}},
+                },
+                {
+                    // These mantissas round down, so adding them together won't
+                    // have any consequences.
                     Number{
                         false,
                         9'999'999'999'999'999'990ULL,
@@ -352,16 +373,24 @@ class Number_test : public beast::unit_test::suite
                 {Number{1'000'000'000'000'000'001, -18},
                  Number{1'000'000'000'000'000'000, -18},
                  Number{1'000'000'000'000'000'000, -36}},
-                {Number{Number::maxRep},
+                {Number{Number::largestMantissa},
                  Number{6, -1},
-                 Number{Number::maxRep - 1}},
-                {Number{false, Number::maxRep + 1, 0, Number::normalized{}},
+                 Number{Number::largestMantissa - 1}},
+                {Number{
+                     false,
+                     Number::largestMantissa + 1,
+                     0,
+                     Number::normalized{}},
                  Number{1, 0},
-                 Number{Number::maxRep / 10 + 1, 1}},
-                {Number{false, Number::maxRep + 1, 0, Number::normalized{}},
+                 Number{Number::largestMantissa / 10 + 1, 1}},
+                {Number{
+                     false,
+                     Number::largestMantissa + 1,
+                     0,
+                     Number::normalized{}},
                  Number{3, 0},
-                 Number{Number::maxRep}},
-                {power(2, 63), Number{3, 0}, Number{Number::maxRep}},
+                 Number{Number::largestMantissa}},
+                {power(2, 63), Number{3, 0}, Number{Number::largestMantissa}},
             });
         auto test = [this](auto const& c) {
             for (auto const& [x, y, z] : c)
@@ -384,14 +413,16 @@ class Number_test : public beast::unit_test::suite
         auto const scale = Number::getMantissaScale();
         testcase << "test_mul " << to_string(scale);
 
-        using Case = std::tuple<Number, Number, Number>;
+        // Case: Factor 1, Factor 2, Expected product, Line number
+        using Case = std::tuple<Number, Number, Number, int>;
         auto test = [this](auto const& c) {
-            for (auto const& [x, y, z] : c)
+            for (auto const& [x, y, z, line] : c)
             {
                 auto const result = x * y;
                 std::stringstream ss;
                 ss << x << " * " << y << " = " << result << ". Expected: " << z;
-                BEAST_EXPECTS(result == z, ss.str());
+                BEAST_EXPECTS(
+                    result == z, ss.str() + " line: " + std::to_string(line));
             }
         };
         auto tests = [&](auto const& cSmall, auto const& cLarge) {
@@ -401,78 +432,105 @@ class Number_test : public beast::unit_test::suite
                 test(cLarge);
         };
         auto const maxMantissa = Number::maxMantissa();
+        auto const maxInternalMantissa =
+            static_cast<std::uint64_t>(
+                static_cast<std::int64_t>(power(10, Number::mantissaLog()))) *
+                10 -
+            1;
 
         saveNumberRoundMode save{Number::setround(Number::to_nearest)};
         {
             auto const cSmall = std::to_array<Case>({
-                {Number{7}, Number{8}, Number{56}},
+                {Number{7}, Number{8}, Number{56}, __LINE__},
                 {Number{1414213562373095, -15},
                  Number{1414213562373095, -15},
-                 Number{2000000000000000, -15}},
+                 Number{2000000000000000, -15},
+                 __LINE__},
                 {Number{-1414213562373095, -15},
                  Number{1414213562373095, -15},
-                 Number{-2000000000000000, -15}},
+                 Number{-2000000000000000, -15},
+                 __LINE__},
                 {Number{-1414213562373095, -15},
                  Number{-1414213562373095, -15},
-                 Number{2000000000000000, -15}},
+                 Number{2000000000000000, -15},
+                 __LINE__},
                 {Number{3214285714285706, -15},
                  Number{3111111111111119, -15},
-                 Number{1000000000000000, -14}},
+                 Number{1000000000000000, -14},
+                 __LINE__},
                 {Number{1000000000000000, -32768},
                  Number{1000000000000000, -32768},
-                 Number{0}},
+                 Number{0},
+                 __LINE__},
                 // Maximum mantissa range
                 {Number{9'999'999'999'999'999, 0},
                  Number{9'999'999'999'999'999, 0},
-                 Number{9'999'999'999'999'998, 16}},
+                 Number{9'999'999'999'999'998, 16},
+                 __LINE__},
             });
             auto const cLarge = std::to_array<Case>({
                 // Note that items with extremely large mantissas need to be
                 // calculated, because otherwise they overflow uint64. Items
                 // from C with larger mantissa
-                {Number{7}, Number{8}, Number{56}},
+                {Number{7}, Number{8}, Number{56}, __LINE__},
                 {Number{1414213562373095, -15},
                  Number{1414213562373095, -15},
-                 Number{1999999999999999862, -18}},
+                 Number{1999999999999999862, -18},
+                 __LINE__},
                 {Number{-1414213562373095, -15},
                  Number{1414213562373095, -15},
-                 Number{-1999999999999999862, -18}},
+                 Number{-1999999999999999862, -18},
+                 __LINE__},
                 {Number{-1414213562373095, -15},
                  Number{-1414213562373095, -15},
-                 Number{1999999999999999862, -18}},
+                 Number{1999999999999999862, -18},
+                 __LINE__},
                 {Number{3214285714285706, -15},
                  Number{3111111111111119, -15},
                  Number{
                      false,
                      9'999'999'999'999'999'579ULL,
                      -18,
-                     Number::normalized{}}},
+                     Number::normalized{}},
+                 __LINE__},
                 {Number{1000000000000000000, -32768},
                  Number{1000000000000000000, -32768},
-                 Number{0}},
+                 Number{0},
+                 __LINE__},
                 // Items from cSmall expanded for the larger mantissa,
                 // except duplicates. Sadly, it looks like sqrt(2)^2 != 2
                 // with higher precision
                 {Number{1414213562373095049, -18},
                  Number{1414213562373095049, -18},
-                 Number{2000000000000000001, -18}},
+                 Number{2000000000000000001, -18},
+                 __LINE__},
                 {Number{-1414213562373095048, -18},
                  Number{1414213562373095048, -18},
-                 Number{-1999999999999999998, -18}},
+                 Number{-1999999999999999998, -18},
+                 __LINE__},
                 {Number{-1414213562373095048, -18},
                  Number{-1414213562373095049, -18},
-                 Number{1999999999999999999, -18}},
+                 Number{1999999999999999999, -18},
+                 __LINE__},
                 {Number{3214285714285714278, -18},
                  Number{3111111111111111119, -18},
-                 Number{10, 0}},
-                // Maximum mantissa range - rounds up to 1e19
+                 Number{10, 0},
+                 __LINE__},
+                // Maximum internal mantissa range - rounds up to 1e19
+                {Number{false, maxInternalMantissa, 0, Number::normalized{}},
+                 Number{false, maxInternalMantissa, 0, Number::normalized{}},
+                 Number{1, 38},
+                 __LINE__},
+                // Maximum actual mantissa range - same as int64 range
                 {Number{false, maxMantissa, 0, Number::normalized{}},
                  Number{false, maxMantissa, 0, Number::normalized{}},
-                 Number{1, 38}},
+                 Number{85'070'591'730'234'615'85, 19},
+                 __LINE__},
                 // Maximum int64 range
-                {Number{Number::maxRep, 0},
-                 Number{Number::maxRep, 0},
-                 Number{85'070'591'730'234'615'85, 19}},
+                {Number{Number::largestMantissa, 0},
+                 Number{Number::largestMantissa, 0},
+                 Number{85'070'591'730'234'615'85, 19},
+                 __LINE__},
             });
             tests(cSmall, cLarge);
         }
@@ -481,76 +539,100 @@ class Number_test : public beast::unit_test::suite
                  << " towards_zero";
         {
             auto const cSmall = std::to_array<Case>(
-                {{Number{7}, Number{8}, Number{56}},
+                {{Number{7}, Number{8}, Number{56}, __LINE__},
                  {Number{1414213562373095, -15},
                   Number{1414213562373095, -15},
-                  Number{1999999999999999, -15}},
+                  Number{1999999999999999, -15},
+                  __LINE__},
                  {Number{-1414213562373095, -15},
                   Number{1414213562373095, -15},
-                  Number{-1999999999999999, -15}},
+                  Number{-1999999999999999, -15},
+                  __LINE__},
                  {Number{-1414213562373095, -15},
                   Number{-1414213562373095, -15},
-                  Number{1999999999999999, -15}},
+                  Number{1999999999999999, -15},
+                  __LINE__},
                  {Number{3214285714285706, -15},
                   Number{3111111111111119, -15},
-                  Number{9999999999999999, -15}},
+                  Number{9999999999999999, -15},
+                  __LINE__},
                  {Number{1000000000000000, -32768},
                   Number{1000000000000000, -32768},
-                  Number{0}}});
+                  Number{0},
+                  __LINE__}});
             auto const cLarge = std::to_array<Case>(
                 // Note that items with extremely large mantissas need to be
                 // calculated, because otherwise they overflow uint64. Items
                 // from C with larger mantissa
                 {
-                    {Number{7}, Number{8}, Number{56}},
+                    {Number{7}, Number{8}, Number{56}, __LINE__},
                     {Number{1414213562373095, -15},
                      Number{1414213562373095, -15},
-                     Number{1999999999999999861, -18}},
+                     Number{1999999999999999861, -18},
+                     __LINE__},
                     {Number{-1414213562373095, -15},
                      Number{1414213562373095, -15},
-                     Number{-1999999999999999861, -18}},
+                     Number{-1999999999999999861, -18},
+                     __LINE__},
                     {Number{-1414213562373095, -15},
                      Number{-1414213562373095, -15},
-                     Number{1999999999999999861, -18}},
+                     Number{1999999999999999861, -18},
+                     __LINE__},
                     {Number{3214285714285706, -15},
                      Number{3111111111111119, -15},
                      Number{
                          false,
                          9999999999999999579ULL,
                          -18,
-                         Number::normalized{}}},
+                         Number::normalized{}},
+                     __LINE__},
                     {Number{1000000000000000000, -32768},
                      Number{1000000000000000000, -32768},
-                     Number{0}},
+                     Number{0},
+                     __LINE__},
                     // Items from cSmall expanded for the larger mantissa,
                     // except duplicates. Sadly, it looks like sqrt(2)^2 != 2
                     // with higher precision
                     {Number{1414213562373095049, -18},
                      Number{1414213562373095049, -18},
-                     Number{2, 0}},
+                     Number{2, 0},
+                     __LINE__},
                     {Number{-1414213562373095048, -18},
                      Number{1414213562373095048, -18},
-                     Number{-1999999999999999997, -18}},
+                     Number{-1999999999999999997, -18},
+                     __LINE__},
                     {Number{-1414213562373095048, -18},
                      Number{-1414213562373095049, -18},
-                     Number{1999999999999999999, -18}},
+                     Number{1999999999999999999, -18},
+                     __LINE__},
                     {Number{3214285714285714278, -18},
                      Number{3111111111111111119, -18},
-                     Number{10, 0}},
-                    // Maximum mantissa range - rounds down to maxMantissa/10e1
+                     Number{10, 0},
+                     __LINE__},
+                    // Maximum internal mantissa range - rounds down to
+                    // maxMantissa/10e1
                     // 99'999'999'999'999'999'800'000'000'000'000'000'100
-                    {Number{false, maxMantissa, 0, Number::normalized{}},
-                     Number{false, maxMantissa, 0, Number::normalized{}},
+                    {Number{
+                         false, maxInternalMantissa, 0, Number::normalized{}},
+                     Number{
+                         false, maxInternalMantissa, 0, Number::normalized{}},
                      Number{
                          false,
-                         maxMantissa / 10 - 1,
+                         maxInternalMantissa / 10 - 1,
                          20,
-                         Number::normalized{}}},
+                         Number::normalized{}},
+                     __LINE__},
+                    // Maximum actual mantissa range - same as int64
+                    {Number{false, maxMantissa, 0, Number::normalized{}},
+                     Number{false, maxMantissa, 0, Number::normalized{}},
+                     Number{85'070'591'730'234'615'84, 19},
+                     __LINE__},
                     // Maximum int64 range
                     // 85'070'591'730'234'615'847'396'907'784'232'501'249
-                    {Number{Number::maxRep, 0},
-                     Number{Number::maxRep, 0},
-                     Number{85'070'591'730'234'615'84, 19}},
+                    {Number{Number::largestMantissa, 0},
+                     Number{Number::largestMantissa, 0},
+                     Number{85'070'591'730'234'615'84, 19},
+                     __LINE__},
                 });
             tests(cSmall, cLarge);
         }
@@ -559,76 +641,100 @@ class Number_test : public beast::unit_test::suite
                  << " downward";
         {
             auto const cSmall = std::to_array<Case>(
-                {{Number{7}, Number{8}, Number{56}},
+                {{Number{7}, Number{8}, Number{56}, __LINE__},
                  {Number{1414213562373095, -15},
                   Number{1414213562373095, -15},
-                  Number{1999999999999999, -15}},
+                  Number{1999999999999999, -15},
+                  __LINE__},
                  {Number{-1414213562373095, -15},
                   Number{1414213562373095, -15},
-                  Number{-2000000000000000, -15}},
+                  Number{-2000000000000000, -15},
+                  __LINE__},
                  {Number{-1414213562373095, -15},
                   Number{-1414213562373095, -15},
-                  Number{1999999999999999, -15}},
+                  Number{1999999999999999, -15},
+                  __LINE__},
                  {Number{3214285714285706, -15},
                   Number{3111111111111119, -15},
-                  Number{9999999999999999, -15}},
+                  Number{9999999999999999, -15},
+                  __LINE__},
                  {Number{1000000000000000, -32768},
                   Number{1000000000000000, -32768},
-                  Number{0}}});
+                  Number{0},
+                  __LINE__}});
             auto const cLarge = std::to_array<Case>(
                 // Note that items with extremely large mantissas need to be
                 // calculated, because otherwise they overflow uint64. Items
                 // from C with larger mantissa
                 {
-                    {Number{7}, Number{8}, Number{56}},
+                    {Number{7}, Number{8}, Number{56}, __LINE__},
                     {Number{1414213562373095, -15},
                      Number{1414213562373095, -15},
-                     Number{1999999999999999861, -18}},
+                     Number{1999999999999999861, -18},
+                     __LINE__},
                     {Number{-1414213562373095, -15},
                      Number{1414213562373095, -15},
-                     Number{-1999999999999999862, -18}},
+                     Number{-1999999999999999862, -18},
+                     __LINE__},
                     {Number{-1414213562373095, -15},
                      Number{-1414213562373095, -15},
-                     Number{1999999999999999861, -18}},
+                     Number{1999999999999999861, -18},
+                     __LINE__},
                     {Number{3214285714285706, -15},
                      Number{3111111111111119, -15},
                      Number{
                          false,
                          9'999'999'999'999'999'579ULL,
                          -18,
-                         Number::normalized{}}},
+                         Number::normalized{}},
+                     __LINE__},
                     {Number{1000000000000000000, -32768},
                      Number{1000000000000000000, -32768},
-                     Number{0}},
+                     Number{0},
+                     __LINE__},
                     // Items from cSmall expanded for the larger mantissa,
                     // except duplicates. Sadly, it looks like sqrt(2)^2 != 2
                     // with higher precision
                     {Number{1414213562373095049, -18},
                      Number{1414213562373095049, -18},
-                     Number{2, 0}},
+                     Number{2, 0},
+                     __LINE__},
                     {Number{-1414213562373095048, -18},
                      Number{1414213562373095048, -18},
-                     Number{-1999999999999999998, -18}},
+                     Number{-1999999999999999998, -18},
+                     __LINE__},
                     {Number{-1414213562373095048, -18},
                      Number{-1414213562373095049, -18},
-                     Number{1999999999999999999, -18}},
+                     Number{1999999999999999999, -18},
+                     __LINE__},
                     {Number{3214285714285714278, -18},
                      Number{3111111111111111119, -18},
-                     Number{10, 0}},
-                    // Maximum mantissa range - rounds down to maxMantissa/10e1
+                     Number{10, 0},
+                     __LINE__},
+                    // Maximum internal mantissa range - rounds down to
+                    // maxMantissa/10-1
                     // 99'999'999'999'999'999'800'000'000'000'000'000'100
-                    {Number{false, maxMantissa, 0, Number::normalized{}},
-                     Number{false, maxMantissa, 0, Number::normalized{}},
+                    {Number{
+                         false, maxInternalMantissa, 0, Number::normalized{}},
+                     Number{
+                         false, maxInternalMantissa, 0, Number::normalized{}},
                      Number{
                          false,
-                         maxMantissa / 10 - 1,
+                         maxInternalMantissa / 10 - 1,
                          20,
-                         Number::normalized{}}},
+                         Number::normalized{}},
+                     __LINE__},
+                    // Maximum mantissa range - same as int64
+                    {Number{false, maxMantissa, 0, Number::normalized{}},
+                     Number{false, maxMantissa, 0, Number::normalized{}},
+                     Number{85'070'591'730'234'615'84, 19},
+                     __LINE__},
                     // Maximum int64 range
                     // 85'070'591'730'234'615'847'396'907'784'232'501'249
-                    {Number{Number::maxRep, 0},
-                     Number{Number::maxRep, 0},
-                     Number{85'070'591'730'234'615'84, 19}},
+                    {Number{Number::largestMantissa, 0},
+                     Number{Number::largestMantissa, 0},
+                     Number{85'070'591'730'234'615'84, 19},
+                     __LINE__},
                 });
             tests(cSmall, cLarge);
         }
@@ -637,68 +743,91 @@ class Number_test : public beast::unit_test::suite
                  << " upward";
         {
             auto const cSmall = std::to_array<Case>(
-                {{Number{7}, Number{8}, Number{56}},
+                {{Number{7}, Number{8}, Number{56}, __LINE__},
                  {Number{1414213562373095, -15},
                   Number{1414213562373095, -15},
-                  Number{2000000000000000, -15}},
+                  Number{2000000000000000, -15},
+                  __LINE__},
                  {Number{-1414213562373095, -15},
                   Number{1414213562373095, -15},
-                  Number{-1999999999999999, -15}},
+                  Number{-1999999999999999, -15},
+                  __LINE__},
                  {Number{-1414213562373095, -15},
                   Number{-1414213562373095, -15},
-                  Number{2000000000000000, -15}},
+                  Number{2000000000000000, -15},
+                  __LINE__},
                  {Number{3214285714285706, -15},
                   Number{3111111111111119, -15},
-                  Number{1000000000000000, -14}},
+                  Number{1000000000000000, -14},
+                  __LINE__},
                  {Number{1000000000000000, -32768},
                   Number{1000000000000000, -32768},
-                  Number{0}}});
+                  Number{0},
+                  __LINE__}});
             auto const cLarge = std::to_array<Case>(
                 // Note that items with extremely large mantissas need to be
                 // calculated, because otherwise they overflow uint64. Items
                 // from C with larger mantissa
                 {
-                    {Number{7}, Number{8}, Number{56}},
+                    {Number{7}, Number{8}, Number{56}, __LINE__},
                     {Number{1414213562373095, -15},
                      Number{1414213562373095, -15},
-                     Number{1999999999999999862, -18}},
+                     Number{1999999999999999862, -18},
+                     __LINE__},
                     {Number{-1414213562373095, -15},
                      Number{1414213562373095, -15},
-                     Number{-1999999999999999861, -18}},
+                     Number{-1999999999999999861, -18},
+                     __LINE__},
                     {Number{-1414213562373095, -15},
                      Number{-1414213562373095, -15},
-                     Number{1999999999999999862, -18}},
+                     Number{1999999999999999862, -18},
+                     __LINE__},
                     {Number{3214285714285706, -15},
                      Number{3111111111111119, -15},
-                     Number{999999999999999958, -17}},
+                     Number{999999999999999958, -17},
+                     __LINE__},
                     {Number{1000000000000000000, -32768},
                      Number{1000000000000000000, -32768},
-                     Number{0}},
+                     Number{0},
+                     __LINE__},
                     // Items from cSmall expanded for the larger mantissa,
                     // except duplicates. Sadly, it looks like sqrt(2)^2 != 2
                     // with higher precision
                     {Number{1414213562373095049, -18},
                      Number{1414213562373095049, -18},
-                     Number{2000000000000000001, -18}},
+                     Number{2000000000000000001, -18},
+                     __LINE__},
                     {Number{-1414213562373095048, -18},
                      Number{1414213562373095048, -18},
-                     Number{-1999999999999999997, -18}},
+                     Number{-1999999999999999997, -18},
+                     __LINE__},
                     {Number{-1414213562373095048, -18},
                      Number{-1414213562373095049, -18},
-                     Number{2, 0}},
+                     Number{2, 0},
+                     __LINE__},
                     {Number{3214285714285714278, -18},
                      Number{3111111111111111119, -18},
-                     Number{1000000000000000001, -17}},
-                    // Maximum mantissa range - rounds up to minMantissa*10
-                    // 1e19*1e19=1e38
+                     Number{1000000000000000001, -17},
+                     __LINE__},
+                    // Maximum internal mantissa range - rounds up to
+                    // minMantissa*10 1e19*1e19=1e38
+                    {Number{
+                         false, maxInternalMantissa, 0, Number::normalized{}},
+                     Number{
+                         false, maxInternalMantissa, 0, Number::normalized{}},
+                     Number{1, 38},
+                     __LINE__},
+                    // Maximum mantissa range - same as int64
                     {Number{false, maxMantissa, 0, Number::normalized{}},
                      Number{false, maxMantissa, 0, Number::normalized{}},
-                     Number{1, 38}},
+                     Number{85'070'591'730'234'615'85, 19},
+                     __LINE__},
                     // Maximum int64 range
                     // 85'070'591'730'234'615'847'396'907'784'232'501'249
-                    {Number{Number::maxRep, 0},
-                     Number{Number::maxRep, 0},
-                     Number{85'070'591'730'234'615'85, 19}},
+                    {Number{Number::largestMantissa, 0},
+                     Number{Number::largestMantissa, 0},
+                     Number{85'070'591'730'234'615'85, 19},
+                     __LINE__},
                 });
             tests(cSmall, cLarge);
         }
@@ -971,6 +1100,12 @@ class Number_test : public beast::unit_test::suite
         };
         */
 
+        auto const maxInternalMantissa =
+            static_cast<std::uint64_t>(
+                static_cast<std::int64_t>(power(10, Number::mantissaLog()))) *
+                10 -
+            1;
+
         auto const cSmall = std::to_array<Case>(
             {{Number{2}, 2, Number{1414213562373095049, -18}},
              {Number{2'000'000}, 2, Number{1414213562373095049, -15}},
@@ -982,17 +1117,17 @@ class Number_test : public beast::unit_test::suite
              {Number{0}, 5, Number{0}},
              {Number{5625, -4}, 2, Number{75, -2}}});
         auto const cLarge = std::to_array<Case>({
-            {Number{false, Number::maxMantissa() - 9, -1, Number::normalized{}},
+            {Number{false, maxInternalMantissa - 9, -1, Number::normalized{}},
              2,
              Number{false, 999'999'999'999'999'999, -9, Number::normalized{}}},
-            {Number{false, Number::maxMantissa() - 9, 0, Number::normalized{}},
+            {Number{false, maxInternalMantissa - 9, 0, Number::normalized{}},
              2,
              Number{
                  false, 3'162'277'660'168'379'330, -9, Number::normalized{}}},
-            {Number{Number::maxRep},
+            {Number{Number::largestMantissa},
              2,
              Number{false, 3'037'000'499'976049692, -9, Number::normalized{}}},
-            {Number{Number::maxRep},
+            {Number{Number::largestMantissa},
              4,
              Number{false, 55'108'98747006743627, -14, Number::normalized{}}},
         });
@@ -1042,6 +1177,9 @@ class Number_test : public beast::unit_test::suite
             }
         };
 
+        auto const maxInternalMantissa =
+            power(10, Number::mantissaLog()) * 10 - 1;
+
         auto const cSmall = std::to_array<Number>({
             Number{2},
             Number{2'000'000},
@@ -1051,7 +1189,10 @@ class Number_test : public beast::unit_test::suite
             Number{5, -1},
             Number{0},
             Number{5625, -4},
-            Number{Number::maxRep},
+            Number{Number::largestMantissa},
+            maxInternalMantissa,
+            Number{Number::minMantissa(), 0, Number::unchecked{}},
+            Number{Number::maxMantissa(), 0, Number::unchecked{}},
         });
         test(cSmall);
         bool caught = false;
@@ -1417,20 +1558,20 @@ class Number_test : public beast::unit_test::suite
             case MantissaRange::large:
                 // Test the edges
                 // ((exponent < -(28)) || (exponent > -(8)))))
-                test(Number::min(), "1e-32750");
+                test(Number::min(), "922337203685477581e-32768");
                 test(Number::max(), "9223372036854775807e32768");
                 test(Number::lowest(), "-9223372036854775807e32768");
                 {
                     NumberRoundModeGuard mg(Number::towards_zero);
 
                     auto const maxMantissa = Number::maxMantissa();
-                    BEAST_EXPECT(maxMantissa == 9'999'999'999'999'999'999ULL);
+                    BEAST_EXPECT(maxMantissa == 9'223'372'036'854'775'807ULL);
                     test(
                         Number{false, maxMantissa, 0, Number::normalized{}},
-                        "9999999999999999990");
+                        "9223372036854775807");
                     test(
                         Number{true, maxMantissa, 0, Number::normalized{}},
-                        "-9999999999999999990");
+                        "-9223372036854775807");
 
                     test(
                         Number{std::numeric_limits<std::int64_t>::max(), 0},
@@ -1671,7 +1812,7 @@ class Number_test : public beast::unit_test::suite
             Number const initalXrp{INITIAL_XRP};
             BEAST_EXPECT(initalXrp.exponent() > 0);
 
-            Number const maxInt64{Number::maxRep};
+            Number const maxInt64{Number::largestMantissa};
             BEAST_EXPECT(maxInt64.exponent() > 0);
             // 85'070'591'730'234'615'865'843'651'857'942'052'864 - 38 digits
             BEAST_EXPECT(
@@ -1691,7 +1832,7 @@ class Number_test : public beast::unit_test::suite
             Number const initalXrp{INITIAL_XRP};
             BEAST_EXPECT(initalXrp.exponent() <= 0);
 
-            Number const maxInt64{Number::maxRep};
+            Number const maxInt64{Number::largestMantissa};
             BEAST_EXPECT(maxInt64.exponent() <= 0);
             // 85'070'591'730'234'615'847'396'907'784'232'501'249 - 38 digits
             BEAST_EXPECT(
@@ -1699,16 +1840,247 @@ class Number_test : public beast::unit_test::suite
 
             NumberRoundModeGuard mg(Number::towards_zero);
 
-            auto const maxMantissa = Number::maxMantissa();
-            Number const max =
-                Number{false, maxMantissa, 0, Number::normalized{}};
-            BEAST_EXPECT(max.mantissa() == maxMantissa / 10);
-            BEAST_EXPECT(max.exponent() == 1);
-            // 99'999'999'999'999'999'800'000'000'000'000'000'100 - also 38
-            // digits
-            BEAST_EXPECT((
-                power(max, 2) ==
-                Number{false, maxMantissa / 10 - 1, 20, Number::normalized{}}));
+            {
+                auto const maxInternalMantissa =
+                    static_cast<std::uint64_t>(static_cast<std::int64_t>(
+                        power(10, Number::mantissaLog()))) *
+                        10 -
+                    1;
+
+                // Rounds down to fit under 2^63
+                Number const max =
+                    Number{false, maxInternalMantissa, 0, Number::normalized{}};
+                // No alterations by the accessors
+                BEAST_EXPECT(max.mantissa() == maxInternalMantissa / 10);
+                BEAST_EXPECT(max.exponent() == 1);
+                // 99'999'999'999'999'999'800'000'000'000'000'000'100 - also 38
+                // digits
+                BEAST_EXPECT(
+                    (power(max, 2) ==
+                     Number{
+                         false,
+                         maxInternalMantissa / 10 - 1,
+                         20,
+                         Number::normalized{}}));
+            }
+
+            {
+                auto const maxMantissa = Number::maxMantissa();
+                Number const max =
+                    Number{false, maxMantissa, 0, Number::normalized{}};
+                // No alterations by the accessors
+                BEAST_EXPECT(max.mantissa() == maxMantissa);
+                BEAST_EXPECT(max.exponent() == 0);
+                // 85'070'591'730'234'615'847'396'907'784'232'501'249 - also 38
+                // digits
+                BEAST_EXPECT(
+                    (power(max, 2) ==
+                     Number{
+                         false,
+                         85'070'591'730'234'615'84,
+                         19,
+                         Number::normalized{}}));
+            }
+        }
+    }
+
+    void
+    testNormalizeToRange()
+    {
+        // Test edge-cases of normalizeToRange
+        auto const scale = Number::getMantissaScale();
+        testcase << "normalizeToRange " << to_string(scale);
+
+        auto test = [this](
+                        Number const& n,
+                        auto const rangeMin,
+                        auto const rangeMax,
+                        auto const expectedMantissa,
+                        auto const expectedExponent,
+                        auto const line) {
+            auto const normalized = n.normalizeToRange(rangeMin, rangeMax);
+            BEAST_EXPECTS(
+                normalized.first == expectedMantissa,
+                "Number " + to_string(n) + " scaled to " +
+                    std::to_string(rangeMax) +
+                    ". Expected mantissa:" + std::to_string(expectedMantissa) +
+                    ", got: " + std::to_string(normalized.first) + " @ " +
+                    std::to_string(line));
+            BEAST_EXPECTS(
+                normalized.second == expectedExponent,
+                "Number " + to_string(n) + " scaled to " +
+                    std::to_string(rangeMax) +
+                    ". Expected exponent:" + std::to_string(expectedExponent) +
+                    ", got: " + std::to_string(normalized.second) + " @ " +
+                    std::to_string(line));
+        };
+
+        std::int64_t constexpr iRangeMin = 100;
+        std::int64_t constexpr iRangeMax = 999;
+
+        std::uint64_t constexpr uRangeMin = 100;
+        std::uint64_t constexpr uRangeMax = 999;
+
+        constexpr static MantissaRange largeRange{MantissaRange::large};
+
+        std::int64_t constexpr iBigMin = largeRange.min;
+        std::int64_t constexpr iBigMax = largeRange.max;
+
+        auto const testSuite = [&](Number const& n,
+                                   auto const expectedSmallMantissa,
+                                   auto const expectedSmallExponent,
+                                   auto const expectedLargeMantissa,
+                                   auto const expectedLargeExponent,
+                                   auto const line) {
+            test(
+                n,
+                iRangeMin,
+                iRangeMax,
+                expectedSmallMantissa,
+                expectedSmallExponent,
+                line);
+            test(
+                n,
+                iBigMin,
+                iBigMax,
+                expectedLargeMantissa,
+                expectedLargeExponent,
+                line);
+
+            // Only test non-negative. testing a negative number with an
+            // unsigned range will assert, and asserts can't be tested.
+            if (n.signum() >= 0)
+            {
+                test(
+                    n,
+                    uRangeMin,
+                    uRangeMax,
+                    expectedSmallMantissa,
+                    expectedSmallExponent,
+                    line);
+                test(
+                    n,
+                    largeRange.min,
+                    largeRange.max,
+                    expectedLargeMantissa,
+                    expectedLargeExponent,
+                    line);
+            }
+        };
+
+        {
+            // zero
+            Number const n{0};
+
+            testSuite(
+                n,
+                0,
+                std::numeric_limits<int>::lowest(),
+                0,
+                std::numeric_limits<int>::lowest(),
+                __LINE__);
+        }
+        {
+            // Small positive number
+            Number const n{2};
+
+            testSuite(n, 200, -2, 2'000'000'000'000'000'000, -18, __LINE__);
+        }
+        {
+            // Negative number
+            Number const n{-2};
+
+            testSuite(n, -200, -2, -2'000'000'000'000'000'000, -18, __LINE__);
+        }
+        {
+            // Biggest valid mantissa
+            Number const n{Number::largestMantissa, 0, Number::normalized{}};
+
+            if (scale == MantissaRange::small)
+                // With the small mantissa range, the value rounds up. Because
+                // it rounds up, when scaling up to the full int64 range, it
+                // can't go over the max, so it is one digit smaller than the
+                // full value.
+                testSuite(n, 922, 16, 922'337'203'685'477'600, 1, __LINE__);
+            else
+                testSuite(n, 922, 16, Number::largestMantissa, 0, __LINE__);
+        }
+        {
+            // Biggest valid mantissa + 1
+            Number const n{
+                Number::largestMantissa + 1, 0, Number::normalized{}};
+
+            if (scale == MantissaRange::small)
+                // With the small mantissa range, the value rounds up. Because
+                // it rounds up, when scaling up to the full int64 range, it
+                // can't go over the max, so it is one digit smaller than the
+                // full value.
+                testSuite(n, 922, 16, 922'337'203'685'477'600, 1, __LINE__);
+            else
+                testSuite(n, 922, 16, 922'337'203'685'477'581, 1, __LINE__);
+        }
+        {
+            // Biggest valid mantissa + 2
+            Number const n{
+                Number::largestMantissa + 2, 0, Number::normalized{}};
+
+            if (scale == MantissaRange::small)
+                // With the small mantissa range, the value rounds up. Because
+                // it rounds up, when scaling up to the full int64 range, it
+                // can't go over the max, so it is one digit smaller than the
+                // full value.
+                testSuite(n, 922, 16, 922'337'203'685'477'600, 1, __LINE__);
+            else
+                testSuite(n, 922, 16, 922'337'203'685'477'581, 1, __LINE__);
+        }
+        {
+            // Biggest valid mantissa + 3
+            Number const n{
+                Number::largestMantissa + 3, 0, Number::normalized{}};
+
+            if (scale == MantissaRange::small)
+                // With the small mantissa range, the value rounds up. Because
+                // it rounds up, when scaling up to the full int64 range, it
+                // can't go over the max, so it is one digit smaller than the
+                // full value.
+                testSuite(n, 922, 16, 922'337'203'685'477'600, 1, __LINE__);
+            else
+                testSuite(n, 922, 16, 922'337'203'685'477'581, 1, __LINE__);
+        }
+        {
+            // int64 min
+            Number const n{std::numeric_limits<std::int64_t>::min(), 0};
+
+            if (scale == MantissaRange::small)
+                testSuite(n, -922, 16, -922'337'203'685'477'600, 1, __LINE__);
+            else
+                testSuite(n, -922, 16, -922'337'203'685'477'581, 1, __LINE__);
+        }
+        {
+            // int64 min + 1
+            Number const n{std::numeric_limits<std::int64_t>::min() + 1, 0};
+
+            if (scale == MantissaRange::small)
+                testSuite(n, -922, 16, -922'337'203'685'477'600, 1, __LINE__);
+            else
+                testSuite(n, -922, 16, -9'223'372'036'854'775'807, 0, __LINE__);
+        }
+        {
+            // int64 min - 1
+            // Need to cast to uint, even though we're dealing with a negative
+            // number to avoid overflow and UB
+            Number const n{
+                true,
+                -static_cast<std::uint64_t>(
+                    std::numeric_limits<std::int64_t>::min()) +
+                    1,
+                0,
+                Number::normalized{}};
+
+            if (scale == MantissaRange::small)
+                testSuite(n, -922, 16, -922'337'203'685'477'600, 1, __LINE__);
+            else
+                testSuite(n, -922, 16, -922'337'203'685'477'581, 1, __LINE__);
         }
     }
 
@@ -1739,6 +2111,7 @@ class Number_test : public beast::unit_test::suite
             test_truncate();
             testRounding();
             testInt64();
+            testNormalizeToRange();
         }
     }
 };
diff --git a/src/xrpld/app/misc/LendingHelpers.h b/src/xrpld/app/misc/LendingHelpers.h
index 79fc6175697..5780f764280 100644
--- a/src/xrpld/app/misc/LendingHelpers.h
+++ b/src/xrpld/app/misc/LendingHelpers.h
@@ -176,8 +176,7 @@ getAssetsTotalScale(SLE::const_ref vaultSle)
 {
     if (!vaultSle)
         return Number::minExponent - 1;  // LCOV_EXCL_LINE
-    return STAmount{vaultSle->at(sfAsset), vaultSle->at(sfAssetsTotal)}
-        .exponent();
+    return vaultSle->at(sfAssetsTotal).scale<STAmount>(vaultSle->at(sfAsset));
 }
 
 TER
diff --git a/src/xrpld/app/tx/detail/InvariantCheck.cpp b/src/xrpld/app/tx/detail/InvariantCheck.cpp
index 6fb832a05ea..26895cdd2fe 100644
--- a/src/xrpld/app/tx/detail/InvariantCheck.cpp
+++ b/src/xrpld/app/tx/detail/InvariantCheck.cpp
@@ -2664,8 +2664,13 @@ ValidVault::visitEntry(
     // Number balanceDelta will capture the difference (delta) between "before"
     // state (zero if created) and "after" state (zero if destroyed), so the
     // invariants can validate that the change in account balances matches the
-    // change in vault balances, stored to deltas_ at the end of this function.
-    Number balanceDelta{};
+    // balanceDelta captures the difference (delta) between "before"
+    // state (zero if created) and "after" state (zero if destroyed), and
+    // preserves value scale (exponent) to round values to the same scale during
+    // validation. It is used to validate that the change in account
+    // balances matches the change in vault balances, stored to deltas_ at the
+    // end of this function.
+    DeltaInfo balanceDelta{numZero, std::nullopt};
 
     std::int8_t sign = 0;
     if (before)
@@ -2679,20 +2684,35 @@ ValidVault::visitEntry(
                 // At this moment we have no way of telling if this object holds
                 // vault shares or something else. Save it for finalize.
                 beforeMPTs_.push_back(Shares::make(*before));
-                balanceDelta = static_cast<std::int64_t>(
+                balanceDelta.delta = static_cast<std::int64_t>(
                     before->getFieldU64(sfOutstandingAmount));
+                // MPTs are ints, so the scale is always 0.
+                balanceDelta.scale = 0;
                 sign = 1;
                 break;
             case ltMPTOKEN:
-                balanceDelta =
+                balanceDelta.delta =
                     static_cast<std::int64_t>(before->getFieldU64(sfMPTAmount));
+                // MPTs are ints, so the scale is always 0.
+                balanceDelta.scale = 0;
                 sign = -1;
                 break;
             case ltACCOUNT_ROOT:
-            case ltRIPPLE_STATE:
-                balanceDelta = before->getFieldAmount(sfBalance);
+                balanceDelta.delta = before->getFieldAmount(sfBalance);
+                // Account balance is XRP, which is an int, so the scale is
+                // always 0.
+                balanceDelta.scale = 0;
                 sign = -1;
                 break;
+            case ltRIPPLE_STATE: {
+                auto const amount = before->getFieldAmount(sfBalance);
+                balanceDelta.delta = amount;
+                // Trust Line balances are STAmounts, so we can use the exponent
+                // directly to get the scale.
+                balanceDelta.scale = amount.exponent();
+                sign = -1;
+                break;
+            }
             default:;
         }
     }
@@ -2708,21 +2728,36 @@ ValidVault::visitEntry(
                 // At this moment we have no way of telling if this object holds
                 // vault shares or something else. Save it for finalize.
                 afterMPTs_.push_back(Shares::make(*after));
-                balanceDelta -= Number(
-                    static_cast<std::int64_t>(
-                        after->getFieldU64(sfOutstandingAmount)));
+                balanceDelta.delta -= Number(static_cast<std::int64_t>(
+                    after->getFieldU64(sfOutstandingAmount)));
+                // MPTs are ints, so the scale is always 0.
+                balanceDelta.scale = 0;
                 sign = 1;
                 break;
             case ltMPTOKEN:
-                balanceDelta -= Number(
+                balanceDelta.delta -= Number(
                     static_cast<std::int64_t>(after->getFieldU64(sfMPTAmount)));
+                // MPTs are ints, so the scale is always 0.
+                balanceDelta.scale = 0;
                 sign = -1;
                 break;
             case ltACCOUNT_ROOT:
-            case ltRIPPLE_STATE:
-                balanceDelta -= Number(after->getFieldAmount(sfBalance));
+                balanceDelta.delta -= Number(after->getFieldAmount(sfBalance));
+                // Account balance is XRP, which is an int, so the scale is
+                // always 0.
+                balanceDelta.scale = 0;
+                sign = -1;
+                break;
+            case ltRIPPLE_STATE: {
+                auto const amount = after->getFieldAmount(sfBalance);
+                balanceDelta.delta -= Number(amount);
+                // Trust Line balances are STAmounts, so we can use the exponent
+                // directly to get the scale.
+                if (amount.exponent() > balanceDelta.scale)
+                    balanceDelta.scale = amount.exponent();
                 sign = -1;
                 break;
+            }
             default:;
         }
     }
@@ -2734,7 +2769,14 @@ ValidVault::visitEntry(
     // transferred to the account. We intentionally do not compare balanceDelta
     // against zero, to avoid missing such updates.
     if (sign != 0)
-        deltas_[key] = balanceDelta * sign;
+    {
+        XRPL_ASSERT_PARTS(
+            balanceDelta.scale,
+            "xrpl::ValidVault::visitEntry",
+            "scale initialized");
+        balanceDelta.delta *= sign;
+        deltas_[key] = balanceDelta;
+    }
 }
 
 bool
@@ -3014,13 +3056,15 @@ ValidVault::finalize(
     }
 
     auto const& vaultAsset = afterVault.asset;
-    auto const deltaAssets = [&](AccountID const& id) -> std::optional<Number> {
+    auto const deltaAssets =
+        [&](AccountID const& id) -> std::optional<DeltaInfo> {
         auto const get =  //
-            [&](auto const& it, std::int8_t sign = 1) -> std::optional<Number> {
+            [&](auto const& it,
+                std::int8_t sign = 1) -> std::optional<DeltaInfo> {
             if (it == deltas_.end())
                 return std::nullopt;
 
-            return it->second * sign;
+            return DeltaInfo{it->second.delta * sign, it->second.scale};
         };
 
         return std::visit(
@@ -3041,7 +3085,7 @@ ValidVault::finalize(
             },
             vaultAsset.value());
     };
-    auto const deltaAssetsTxAccount = [&]() -> std::optional<Number> {
+    auto const deltaAssetsTxAccount = [&]() -> std::optional<DeltaInfo> {
         auto ret = deltaAssets(tx[sfAccount]);
         // Nothing returned or not XRP transaction
         if (!ret.has_value() || !vaultAsset.native())
@@ -3052,13 +3096,14 @@ ValidVault::finalize(
             delegate.has_value() && *delegate != tx[sfAccount])
             return ret;
 
-        *ret += fee.drops();
-        if (*ret == zero)
+        ret->delta += fee.drops();
+        if (ret->delta == zero)
             return std::nullopt;
 
         return ret;
     };
-    auto const deltaShares = [&](AccountID const& id) -> std::optional<Number> {
+    auto const deltaShares =
+        [&](AccountID const& id) -> std::optional<DeltaInfo> {
         auto const it = [&]() {
             if (id == afterVault.pseudoId)
                 return deltas_.find(
@@ -3066,7 +3111,7 @@ ValidVault::finalize(
             return deltas_.find(keylet::mptoken(afterVault.shareMPTID, id).key);
         }();
 
-        return it != deltas_.end() ? std::optional<Number>(it->second)
+        return it != deltas_.end() ? std::optional<DeltaInfo>(it->second)
                                    : std::nullopt;
     };
 
@@ -3074,15 +3119,6 @@ ValidVault::finalize(
         return vault.assetsAvailable == 0 && vault.assetsTotal == 0;
     };
 
-    auto const withinDistance = [&](Number const& num1,
-                                    Number const& num2) -> bool {
-        if (vaultAsset.integral())
-            return num1 == num2;
-        // The exponent was set experimentally, based on whether
-        // Loan_test::testWithdrawReflectsUnrealizedLoss unit test fail
-        return withinRelativeDistance(num1, num2, Number{1, -13});
-    };
-
     // Technically this does not need to be a lambda, but it's more
     // convenient thanks to early "return false"; the not-so-nice
     // alternatives are several layers of nested if/else or more complex
@@ -3216,8 +3252,32 @@ ValidVault::finalize(
                     return false;  // That's all we can do
                 }
 
-                auto const vaultDeltaAssets = *maybeVaultDeltaAssets;
-                if (vaultDeltaAssets > tx[sfAmount])
+                // Get the coarsest scale to round calculations to
+                DeltaInfo totalDelta{
+                    afterVault.assetsTotal - beforeVault.assetsTotal,
+                    std::max(
+                        afterVault.assetsTotal.scale<STAmount>(vaultAsset),
+                        beforeVault.assetsTotal.scale<STAmount>(vaultAsset))};
+                DeltaInfo availableDelta{
+                    afterVault.assetsAvailable - beforeVault.assetsAvailable,
+                    std::max(
+                        afterVault.assetsAvailable.scale<STAmount>(vaultAsset),
+                        beforeVault.assetsAvailable.scale<STAmount>(
+                            vaultAsset))};
+                auto const minScale = computeMinScale(
+                    vaultAsset,
+                    {
+                        *maybeVaultDeltaAssets,
+                        totalDelta,
+                        availableDelta,
+                    });
+
+                auto const vaultDeltaAssets = roundToAsset(
+                    vaultAsset, maybeVaultDeltaAssets->delta, minScale);
+                auto const txAmount =
+                    roundToAsset(vaultAsset, tx[sfAmount], minScale);
+
+                if (vaultDeltaAssets > txAmount)
                 {
                     JLOG(j.fatal()) <<  //
                         "Invariant failed: deposit must not change vault "
@@ -3250,7 +3310,14 @@ ValidVault::finalize(
                             "balance";
                         return false;
                     }
-                    auto const accountDeltaAssets = *maybeAccDeltaAssets;
+                    auto const localMinScale = std::max(
+                        minScale,
+                        computeMinScale(vaultAsset, {*maybeAccDeltaAssets}));
+
+                    auto const accountDeltaAssets = roundToAsset(
+                        vaultAsset, maybeAccDeltaAssets->delta, localMinScale);
+                    auto const localVaultDeltaAssets = roundToAsset(
+                        vaultAsset, vaultDeltaAssets, localMinScale);
 
                     if (accountDeltaAssets >= zero)
                     {
@@ -3260,8 +3327,7 @@ ValidVault::finalize(
                         result = false;
                     }
 
-                    if (!withinDistance(
-                            vaultDeltaAssets * -1, accountDeltaAssets))
+                    if (localVaultDeltaAssets * -1 != accountDeltaAssets)
                     {
                         JLOG(j.fatal()) <<  //
                             "Invariant failed: deposit must change vault and "
@@ -3289,7 +3355,7 @@ ValidVault::finalize(
                 }
                 // We don't need to round shares, they are integral MPT
                 auto const& accountDeltaShares = *maybeAccDeltaShares;
-                if (accountDeltaShares <= zero)
+                if (accountDeltaShares.delta <= zero)
                 {
                     JLOG(j.fatal()) <<  //
                         "Invariant failed: deposit must increase depositor "
@@ -3299,7 +3365,8 @@ ValidVault::finalize(
 
                 auto const maybeVaultDeltaShares =
                     deltaShares(afterVault.pseudoId);
-                if (!maybeVaultDeltaShares || *maybeVaultDeltaShares == zero)
+                if (!maybeVaultDeltaShares ||
+                    maybeVaultDeltaShares->delta == zero)
                 {
                     JLOG(j.fatal()) <<  //
                         "Invariant failed: deposit must change vault shares";
@@ -3308,7 +3375,7 @@ ValidVault::finalize(
 
                 // We don't need to round shares, they are integral MPT
                 auto const& vaultDeltaShares = *maybeVaultDeltaShares;
-                if (vaultDeltaShares * -1 != accountDeltaShares)
+                if (vaultDeltaShares.delta * -1 != accountDeltaShares.delta)
                 {
                     JLOG(j.fatal()) <<  //
                         "Invariant failed: deposit must change depositor and "
@@ -3316,18 +3383,22 @@ ValidVault::finalize(
                     result = false;
                 }
 
-                auto const assetTotalDelta =
-                    afterVault.assetsTotal - beforeVault.assetsTotal;
-                if (!withinDistance(assetTotalDelta, vaultDeltaAssets))
+                auto const assetTotalDelta = roundToAsset(
+                    vaultAsset,
+                    afterVault.assetsTotal - beforeVault.assetsTotal,
+                    minScale);
+                if (assetTotalDelta != vaultDeltaAssets)
                 {
                     JLOG(j.fatal()) << "Invariant failed: deposit and assets "
                                        "outstanding must add up";
                     result = false;
                 }
 
-                auto const assetAvailableDelta =
-                    afterVault.assetsAvailable - beforeVault.assetsAvailable;
-                if (!withinDistance(assetAvailableDelta, vaultDeltaAssets))
+                auto const assetAvailableDelta = roundToAsset(
+                    vaultAsset,
+                    afterVault.assetsAvailable - beforeVault.assetsAvailable,
+                    minScale);
+                if (assetAvailableDelta != vaultDeltaAssets)
                 {
                     JLOG(j.fatal()) << "Invariant failed: deposit and assets "
                                        "available must add up";
@@ -3355,7 +3426,24 @@ ValidVault::finalize(
                     return false;  // That's all we can do
                 }
 
-                auto const vaultPseudoDeltaAssets = *maybeVaultDeltaAssets;
+                // Get the most coarse scale to round calculations to
+                auto const totalDelta = DeltaInfo{
+                    afterVault.assetsTotal - beforeVault.assetsTotal,
+                    std::max(
+                        afterVault.assetsTotal.scale<STAmount>(vaultAsset),
+                        beforeVault.assetsTotal.scale<STAmount>(vaultAsset))};
+                auto const availableDelta = DeltaInfo{
+                    afterVault.assetsAvailable - beforeVault.assetsAvailable,
+                    std::max(
+                        afterVault.assetsAvailable.scale<STAmount>(vaultAsset),
+                        beforeVault.assetsAvailable.scale<STAmount>(
+                            vaultAsset))};
+                auto const minScale = computeMinScale(
+                    vaultAsset,
+                    {*maybeVaultDeltaAssets, totalDelta, availableDelta});
+
+                auto const vaultPseudoDeltaAssets = roundToAsset(
+                    vaultAsset, maybeVaultDeltaAssets->delta, minScale);
 
                 if (vaultPseudoDeltaAssets >= zero)
                 {
@@ -3377,7 +3465,7 @@ ValidVault::finalize(
                 {
                     auto const maybeAccDelta = deltaAssetsTxAccount();
                     auto const maybeOtherAccDelta =
-                        [&]() -> std::optional<Number> {
+                        [&]() -> std::optional<DeltaInfo> {
                         if (auto const destination = tx[~sfDestination];
                             destination && *destination != tx[sfAccount])
                             return deltaAssets(*destination);
@@ -3396,7 +3484,16 @@ ValidVault::finalize(
                     auto const destinationDelta =  //
                         maybeAccDelta ? *maybeAccDelta : *maybeOtherAccDelta;
 
-                    if (destinationDelta <= zero)
+                    // the scale of destinationDelta can be coarser than
+                    // minScale, so we take that into account when rounding
+                    auto const localMinScale = std::max(
+                        minScale,
+                        computeMinScale(vaultAsset, {destinationDelta}));
+
+                    auto const roundedDestinationDelta = roundToAsset(
+                        vaultAsset, destinationDelta.delta, localMinScale);
+
+                    if (roundedDestinationDelta <= zero)
                     {
                         JLOG(j.fatal()) <<  //
                             "Invariant failed: withdrawal must increase "
@@ -3404,8 +3501,9 @@ ValidVault::finalize(
                         result = false;
                     }
 
-                    if (!withinDistance(
-                            vaultPseudoDeltaAssets * -1, destinationDelta))
+                    auto const localPseudoDeltaAssets = roundToAsset(
+                        vaultAsset, vaultPseudoDeltaAssets, localMinScale);
+                    if (localPseudoDeltaAssets * -1 != roundedDestinationDelta)
                     {
                         JLOG(j.fatal()) <<  //
                             "Invariant failed: withdrawal must change vault "
@@ -3423,7 +3521,7 @@ ValidVault::finalize(
                     return false;
                 }
 
-                if (*accountDeltaShares >= zero)
+                if (accountDeltaShares->delta >= zero)
                 {
                     JLOG(j.fatal()) <<  //
                         "Invariant failed: withdrawal must decrease depositor "
@@ -3432,14 +3530,14 @@ ValidVault::finalize(
                 }
                 // We don't need to round shares, they are integral MPT
                 auto const vaultDeltaShares = deltaShares(afterVault.pseudoId);
-                if (!vaultDeltaShares || *vaultDeltaShares == zero)
+                if (!vaultDeltaShares || vaultDeltaShares->delta == zero)
                 {
                     JLOG(j.fatal()) <<  //
                         "Invariant failed: withdrawal must change vault shares";
                     return false;  // That's all we can do
                 }
 
-                if (*vaultDeltaShares * -1 != *accountDeltaShares)
+                if (vaultDeltaShares->delta * -1 != accountDeltaShares->delta)
                 {
                     JLOG(j.fatal()) <<  //
                         "Invariant failed: withdrawal must change depositor "
@@ -3447,20 +3545,24 @@ ValidVault::finalize(
                     result = false;
                 }
 
-                auto const assetTotalDelta =
-                    afterVault.assetsTotal - beforeVault.assetsTotal;
+                auto const assetTotalDelta = roundToAsset(
+                    vaultAsset,
+                    afterVault.assetsTotal - beforeVault.assetsTotal,
+                    minScale);
                 // Note, vaultBalance is negative (see check above)
-                if (!withinDistance(assetTotalDelta, vaultPseudoDeltaAssets))
+                if (assetTotalDelta != vaultPseudoDeltaAssets)
                 {
                     JLOG(j.fatal()) << "Invariant failed: withdrawal and "
                                        "assets outstanding must add up";
                     result = false;
                 }
 
-                auto const assetAvailableDelta =
-                    afterVault.assetsAvailable - beforeVault.assetsAvailable;
-                if (!withinDistance(
-                        assetAvailableDelta, vaultPseudoDeltaAssets))
+                auto const assetAvailableDelta = roundToAsset(
+                    vaultAsset,
+                    afterVault.assetsAvailable - beforeVault.assetsAvailable,
+                    minScale);
+
+                if (assetAvailableDelta != vaultPseudoDeltaAssets)
                 {
                     JLOG(j.fatal()) << "Invariant failed: withdrawal and "
                                        "assets available must add up";
@@ -3498,7 +3600,25 @@ ValidVault::finalize(
                     deltaAssets(afterVault.pseudoId);
                 if (maybeVaultDeltaAssets)
                 {
-                    auto const vaultDeltaAssets = *maybeVaultDeltaAssets;
+                    auto const totalDelta = DeltaInfo{
+                        afterVault.assetsTotal - beforeVault.assetsTotal,
+                        std::max(
+                            afterVault.assetsTotal.scale<STAmount>(vaultAsset),
+                            beforeVault.assetsTotal.scale<STAmount>(
+                                vaultAsset))};
+                    auto const availableDelta = DeltaInfo{
+                        afterVault.assetsAvailable -
+                            beforeVault.assetsAvailable,
+                        std::max(
+                            afterVault.assetsAvailable.scale<STAmount>(
+                                vaultAsset),
+                            beforeVault.assetsAvailable.scale<STAmount>(
+                                vaultAsset))};
+                    auto const minScale = computeMinScale(
+                        vaultAsset,
+                        {*maybeVaultDeltaAssets, totalDelta, availableDelta});
+                    auto const vaultDeltaAssets = roundToAsset(
+                        vaultAsset, maybeVaultDeltaAssets->delta, minScale);
                     if (vaultDeltaAssets >= zero)
                     {
                         JLOG(j.fatal()) <<  //
@@ -3507,22 +3627,24 @@ ValidVault::finalize(
                         result = false;
                     }
 
-                    auto const assetsTotalDelta =
-                        afterVault.assetsTotal - beforeVault.assetsTotal;
+                    auto const assetsTotalDelta = roundToAsset(
+                        vaultAsset,
+                        afterVault.assetsTotal - beforeVault.assetsTotal,
+                        minScale);
                     if (assetsTotalDelta != vaultDeltaAssets)
-                        if (!withinDistance(assetsTotalDelta, vaultDeltaAssets))
-                        {
-                            JLOG(j.fatal()) <<  //
-                                "Invariant failed: clawback and assets "
-                                "outstanding "
-                                "must add up";
-                            result = false;
-                        }
-
-                    auto const assetAvailableDelta =
+                    {
+                        JLOG(j.fatal()) <<  //
+                            "Invariant failed: clawback and assets outstanding "
+                            "must add up";
+                        result = false;
+                    }
+
+                    auto const assetAvailableDelta = roundToAsset(
+                        vaultAsset,
                         afterVault.assetsAvailable -
-                        beforeVault.assetsAvailable;
-                    if (!withinDistance(assetAvailableDelta, vaultDeltaAssets))
+                            beforeVault.assetsAvailable,
+                        minScale);
+                    if (assetAvailableDelta != vaultDeltaAssets)
                     {
                         JLOG(j.fatal()) <<  //
                             "Invariant failed: clawback and assets available "
@@ -3545,7 +3667,7 @@ ValidVault::finalize(
                         "Invariant failed: clawback must change holder shares";
                     return false;  // That's all we can do
                 }
-                if (*maybeAccountDeltaShares >= zero)
+                if (maybeAccountDeltaShares->delta >= zero)
                 {
                     JLOG(j.fatal()) <<  //
                         "Invariant failed: clawback must decrease holder "
@@ -3555,14 +3677,15 @@ ValidVault::finalize(
 
                 // We don't need to round shares, they are integral MPT
                 auto const vaultDeltaShares = deltaShares(afterVault.pseudoId);
-                if (!vaultDeltaShares || *vaultDeltaShares == zero)
+                if (!vaultDeltaShares || vaultDeltaShares->delta == zero)
                 {
                     JLOG(j.fatal()) <<  //
                         "Invariant failed: clawback must change vault shares";
                     return false;  // That's all we can do
                 }
 
-                if (*vaultDeltaShares * -1 != *maybeAccountDeltaShares)
+                if (vaultDeltaShares->delta * -1 !=
+                    maybeAccountDeltaShares->delta)
                 {
                     JLOG(j.fatal()) <<  //
                         "Invariant failed: clawback must change holder and "
@@ -3599,4 +3722,24 @@ ValidVault::finalize(
 
     return true;
 }
+
+[[nodiscard]] std::int32_t
+ValidVault::computeMinScale(
+    Asset const& asset,
+    std::initializer_list<DeltaInfo const> numbers)
+{
+    if (numbers.size() == 0)
+        return 0;
+
+    auto const max = std::max_element(
+        numbers.begin(),
+        numbers.end(),
+        [](auto const& a, auto const& b) -> bool { return a.scale < b.scale; });
+    XRPL_ASSERT_PARTS(
+        max->scale,
+        "xrpl::ValidVault::computeMinScale",
+        "scale set for destinationDelta");
+    return max->scale.value_or(STAmount::cMaxOffset);
+}
+
 }  // namespace xrpl
diff --git a/src/xrpld/app/tx/detail/InvariantCheck.h b/src/xrpld/app/tx/detail/InvariantCheck.h
index 83152f74859..574c8f7a061 100644
--- a/src/xrpld/app/tx/detail/InvariantCheck.h
+++ b/src/xrpld/app/tx/detail/InvariantCheck.h
@@ -879,11 +879,19 @@ class ValidVault
         Shares static make(SLE const&);
     };
 
+public:
+    struct DeltaInfo final
+    {
+        Number delta = numZero;
+        std::optional<int> scale;
+    };
+
+private:
     std::vector<Vault> afterVault_ = {};
     std::vector<Shares> afterMPTs_ = {};
     std::vector<Vault> beforeVault_ = {};
     std::vector<Shares> beforeMPTs_ = {};
-    std::unordered_map<uint256, Number> deltas_ = {};
+    std::unordered_map<uint256, DeltaInfo> deltas_ = {};
 
 public:
     void
@@ -899,6 +907,12 @@ class ValidVault
         XRPAmount const,
         ReadView const&,
         beast::Journal const&);
+
+    // Compute the coarsest scale required to represent all numbers
+    [[nodiscard]] static std::int32_t
+    computeMinScale(
+        Asset const& asset,
+        std::initializer_list<DeltaInfo const> numbers);
 };
 
 // additional invariant checks can be declared above and then added to this
diff --git a/src/xrpld/app/tx/detail/LoanBrokerCoverWithdraw.cpp b/src/xrpld/app/tx/detail/LoanBrokerCoverWithdraw.cpp
index 5d4d2053ed3..baafc6f2c08 100644
--- a/src/xrpld/app/tx/detail/LoanBrokerCoverWithdraw.cpp
+++ b/src/xrpld/app/tx/detail/LoanBrokerCoverWithdraw.cpp
@@ -125,7 +125,7 @@ LoanBrokerCoverWithdraw::preclaim(PreclaimContext const& ctx)
             tenthBipsOfValue(
                 currentDebtTotal,
                 TenthBips32(sleBroker->at(sfCoverRateMinimum))),
-            currentDebtTotal.exponent());
+            currentDebtTotal.scale<STAmount>(vaultAsset));
     }();
     if (coverAvail < amount)
         return tecINSUFFICIENT_FUNDS;