diff --git a/PreciseNumber.Test/PreciseNumberTests.cs b/PreciseNumber.Test/PreciseNumberTests.cs
index 10ea1d1..5e5a847 100644
--- a/PreciseNumber.Test/PreciseNumberTests.cs
+++ b/PreciseNumber.Test/PreciseNumberTests.cs
@@ -1033,6 +1033,37 @@ public void TestRoundRoundsHalfAwayFromZeroOnTheDroppedDigits()
 		}
 	}
 
+	[TestMethod]
+	public void TestRoundToNegativeDecimalsDoesNotDependOnHowTheValueIsStored()
+	{
+		static PreciseNumber P(string text) => PreciseNumber.Parse(text, CultureInfo.InvariantCulture);
+
+		// Integers are stored with trailing zeros moved into a positive exponent, so "1230" is 123 at
+		// exponent 1. Rounding used to derive the dropped digits from the decimal places alone, which
+		// only worked when the value had a fractional part.
+		(string Input, int Decimals, string Expected)[] cases =
+		[
+			("1234.5", -2, "1200"),
+			("1234", -2, "1200"),
+			("1230", -2, "1200"),
+			("1250", -2, "1300"),
+			("1500", -3, "2000"),
+			("-1500", -3, "-2000"),
+			("1499", -3, "1000"),
+			("400", -3, "0"),
+			("1200", -2, "1200"),
+			("1234", 0, "1234"),
+			("1230", 2, "1230"),
+			("7", -1, "10"),
+		];
+
+		foreach ((string input, int decimals, string expected) in cases)
+		{
+			Assert.AreEqual(P(expected), P(input).Round(decimals), $"{input} to {decimals} decimal places");
+			Assert.AreEqual(P(expected), PreciseNumber.Round(P(input), decimals), $"static Round of {input} to {decimals} decimal places");
+		}
+	}
+
 	[TestMethod]
 	public void TestMakeCommonizedAndGetExponent()
 	{
diff --git a/PreciseNumber/PreciseNumber.cs b/PreciseNumber/PreciseNumber.cs
index fc17624..20a29ee 100644
--- a/PreciseNumber/PreciseNumber.cs
+++ b/PreciseNumber/PreciseNumber.cs
@@ -544,21 +544,28 @@ public static string ToString(PreciseNumber number, string? format, IFormatProvi
 	/// </summary>
 	/// <param name="decimalDigits">The number of decimal digits to round to.</param>
 	/// <returns>A new instance of <see cref="PreciseNumber"/> rounded to the specified number of decimal digits.</returns>
-	/// <remarks>Rounds half away from zero, so 1.235 becomes 1.24 and 1.2349 becomes 1.23.</remarks>
+	/// <remarks>
+	/// Rounds half away from zero, so 1.235 becomes 1.24 and 1.2349 becomes 1.23. A negative
+	/// <paramref name="decimalDigits"/> rounds to a place left of the units, so 1234 rounded to -2
+	/// becomes 1200 and 1500 rounded to -3 becomes 2000.
+	/// </remarks>
 	public PreciseNumber Round(int decimalDigits)
 	{
-		long currentDecimalDigits = CountDecimalDigits();
-		long decimalDifference = long.Abs(decimalDigits - currentDecimalDigits);
-		if (currentDecimalDigits > decimalDigits && decimalDifference > 0)
+		// The requested place, as the exponent of its digit. Anything stored below it is dropped.
+		// Working from this rather than from CountDecimalDigits keeps the arithmetic right whatever
+		// the sign of the stored exponent: a value with trailing zeros, stored with a positive
+		// exponent, has its last digit that many places left of the units.
+		long targetExponent = -(long)decimalDigits;
+		if (Exponent < targetExponent)
 		{
 			// Dropping one digit more than the significand holds always leaves zero, so there is
 			// never a reason to raise ten to a wider power than that, however far below the
 			// requested place the value sits.
-			int droppedDigits = (int)long.Min(decimalDifference, SignificantDigits + 1);
+			int droppedDigits = (int)long.Min(targetExponent - Exponent, SignificantDigits + 1);
 			BigInteger newSignificand = DropDigitsRoundingHalfAwayFromZero(Significand, droppedDigits);
 			int newExponent = newSignificand.IsZero
 				? 0
-				: Exponent - int.CopySign(droppedDigits, Exponent);
+				: checked(Exponent + droppedDigits);
 			return new PreciseNumber(newExponent, newSignificand);
 		}