diff --git a/test/src/lib/implementation/LibDecimalFloatImplementation.div.t.sol b/test/src/lib/implementation/LibDecimalFloatImplementation.div.t.sol
index 3a757e5..d844073 100644
--- a/test/src/lib/implementation/LibDecimalFloatImplementation.div.t.sol
+++ b/test/src/lib/implementation/LibDecimalFloatImplementation.div.t.sol
@@ -199,4 +199,120 @@ contract LibDecimalFloatImplementationDivTest is Test {
             ++di;
         }
     }
+
+    /// Asserts the round trip identity `(a / b) * b == a` (as a value, via `eq`)
+    /// for exact divisions. This pins both the quotient mantissa AND the exponent
+    /// bookkeeping (including the `adjustExponent` constant selected for `b`),
+    /// because a wrong `adjustExponent` would scale the quotient by a power of
+    /// ten and break the equality.
+    function checkDivInverse(int256 signedCoefficientA, int256 exponentA, int256 signedCoefficientB, int256 exponentB)
+        internal
+        pure
+    {
+        (int256 q, int256 qe) =
+            LibDecimalFloatImplementation.div(signedCoefficientA, exponentA, signedCoefficientB, exponentB);
+        (int256 back, int256 backE) = LibDecimalFloatImplementation.mul(q, qe, signedCoefficientB, exponentB);
+        assertTrue(LibDecimalFloatImplementation.eq(back, backE, signedCoefficientA, exponentA), "(a / b) * b == a");
+    }
+
+    /// The scaling logic inside `div` selects an `adjustExponent` based on a
+    /// binary search over the order of magnitude of the (maximized) divisor
+    /// coefficient. The smaller-than-`1e75` leaves of that search are only
+    /// reachable when the divisor cannot be maximized because its exponent sits
+    /// at `type(int256).min`, leaving the coefficient at its given magnitude.
+    ///
+    /// Each row below places `9 * 10^j / 3 * 10^j` (an exact `3`) with the
+    /// divisor pinned to `type(int256).min` so that `3 * 10^j` lands strictly
+    /// inside one sub-range of the binary search. The quotient mantissa is
+    /// therefore always the maximized `3` (i.e. `3e75`) and the round trip must
+    /// hold regardless of which sub-range was selected.
+    function testDivAdjustExponentLeaves() external pure {
+        int256 min = type(int256).min;
+        // [div by, lands in sub-range)
+        int256[16] memory divisors = [
+            int256(3), // < 1e5
+            3e6, // [1e5, 1e10)
+            3e11, // [1e10, 1e14)
+            3e15, // [1e14, 1e19)
+            3e20, // [1e19, 1e23)
+            3e24, // [1e23, 1e28)
+            3e29, // [1e28, 1e33)
+            3e34, // [1e33, 1e38)
+            3e39, // [1e38, 1e43)
+            3e44, // [1e43, 1e48)
+            3e49, // [1e48, 1e53)
+            3e54, // [1e53, 1e58)
+            3e59, // [1e58, 1e63)
+            3e64, // [1e63, 1e68)
+            3e69, // [1e68, 1e73)
+            3e73 // [1e73, 1e75) the "noop" leaf that keeps the starting 1e76 scale
+        ];
+        for (uint256 i = 0; i < divisors.length; i++) {
+            int256 numerator = 3 * divisors[i];
+            (int256 q, int256 qe) = LibDecimalFloatImplementation.div(numerator, 0, divisors[i], min);
+            // A single significant figure "3" maximizes to 76 digits, i.e. 3e75.
+            assertEq(q, 3e75, "quotient mantissa");
+            // The exponent is enormous (close to -type(int256).min) so it is
+            // pinned by the round trip rather than a literal here.
+            (int256 back, int256 backE) = LibDecimalFloatImplementation.mul(q, qe, divisors[i], min);
+            assertTrue(LibDecimalFloatImplementation.eq(back, backE, numerator, 0), "round trip");
+        }
+    }
+
+    /// Each binary search boundary is `< scale` (strict), so a divisor sitting
+    /// exactly on a power-of-ten boundary falls into the higher sub-range. This
+    /// exercises the boundary comparisons themselves rather than the interiors.
+    function testDivAdjustExponentBoundaries() external pure {
+        int256 min = type(int256).min;
+        int256[14] memory boundaries =
+            [int256(1e5), 1e10, 1e14, 1e19, 1e23, 1e28, 1e33, 1e38, 1e43, 1e48, 1e53, 1e58, 1e63, 1e68];
+        for (uint256 i = 0; i < boundaries.length; i++) {
+            // A divisor of exactly 10^k divides any 10^m numerator exactly.
+            checkDivInverse(boundaries[i], 0, boundaries[i], min);
+        }
+    }
+
+    /// When the maximized divisor coefficient is full (>= 1e75) but still less
+    /// than 1e76, `div` takes the dedicated `scale = 1e75` / `adjustExponent = 75`
+    /// branch rather than the binary search.
+    function testDivAdjustExponentFullDivisor() external pure {
+        int256 min = type(int256).min;
+        // 3e75 has 76 digits, so 3e75 / 1e75 == 3 != 0 => "full", but 3e75 < 1e76.
+        (int256 q, int256 qe) = LibDecimalFloatImplementation.div(9e75, 0, 3e75, min);
+        assertEq(q, 3e75, "full divisor quotient mantissa");
+        (int256 back, int256 backE) = LibDecimalFloatImplementation.mul(q, qe, 3e75, min);
+        assertTrue(LibDecimalFloatImplementation.eq(back, backE, 9e75, 0), "full divisor round trip");
+    }
+
+    /// When the maximized divisor coefficient is already >= 1e76 the whole
+    /// scaling block is skipped and the starting `adjustExponent = 76` is used.
+    function testDivAdjustExponentLargeDivisor() external pure {
+        int256 min = type(int256).min;
+        // 3e76 >= 1e76 so the `if (signedCoefficientBAbs < scale)` block is skipped.
+        checkDivInverse(3e76, 0, 3e76, min);
+    }
+
+    /// The exponent adjustment is first applied to `exponentA`. When `exponentA`
+    /// is already at `type(int256).min` the leftover adjustment spills over onto
+    /// `exponentB` instead.
+    function testDivAdjustExponentSpillsToExponentB() external pure {
+        int256 min = type(int256).min;
+        // 1e76 is full at any exponent, so fullA holds even at min, avoiding the
+        // MaximizeOverflow revert while forcing the spill-to-exponentB path.
+        // 1e76 * 10^min / (3e75 * 10^min) == 10/3.
+        checkDiv(1e76, min, 3e75, min, THREES, -75);
+    }
+
+    /// When the adjustment cannot be applied to `exponentA` (already at the
+    /// minimum) and applying the remainder to `exponentB` would overflow it past
+    /// `type(int256).max`, `div` returns maximized zero.
+    function testDivAdjustExponentSpillOverflowReturnsZero() external pure {
+        checkDiv(1e76, type(int256).min, 3e75, type(int256).max, 0, 0);
+    }
+
+    /// A division whose true exponent underflows below what a single result can
+    /// represent returns maximized zero.
+    function testDivUnderflowReturnsZero() external pure {
+        checkDiv(1e76, type(int256).min, 3, type(int256).max, 0, 0);
+    }
 }