diff --git a/SignificantNumber.Test/SignificantNumberExactOperandTests.cs b/SignificantNumber.Test/SignificantNumberExactOperandTests.cs
new file mode 100644
index 0000000..a129541
--- /dev/null
+++ b/SignificantNumber.Test/SignificantNumberExactOperandTests.cs
@@ -0,0 +1,100 @@
+// Copyright (c) 2023-2026 ktsu-dev contributors
+
+namespace SignificantNumber.Test;
+
+using System.Globalization;
+using System.Numerics;
+using ktsu.SignificantNumber;
+
+/// <summary>
+/// Covers arithmetic and comparison where both operands are -1, 0, or 1, which have unlimited precision.
+/// </summary>
+[TestClass]
+public class SignificantNumberExactOperandTests
+{
+	private static SignificantNumber Parse(string text) =>
+		SignificantNumber.Parse(text, NumberStyles.Float, CultureInfo.InvariantCulture);
+
+	private static T Square<T>(T value)
+		where T : INumber<T> =>
+		value * value;
+
+	[TestMethod]
+	[DataRow("1", "0")]
+	[DataRow("-1", "0")]
+	[DataRow("0", "0")]
+	[DataRow("0", "1")]
+	[DataRow("0", "-1")]
+	public void Multiply_ByZero_ReturnsZero(string left, string right) =>
+		Assert.AreEqual(SignificantNumber.Zero, Parse(left) * Parse(right));
+
+	[TestMethod]
+	public void Multiply_DefaultByDefault_ReturnsZero() =>
+		Assert.AreEqual(SignificantNumber.Zero, default(SignificantNumber) * default(SignificantNumber));
+
+	[TestMethod]
+	public void Square_OfZeroThroughGenericMath_ReturnsZero() =>
+		Assert.AreEqual(SignificantNumber.Zero, Square(SignificantNumber.Zero));
+
+	[TestMethod]
+	public void Multiply_ExactOperands_IsCommutativeAndExact()
+	{
+		string[] values = ["-1", "0", "1"];
+		foreach (string left in values)
+		{
+			foreach (string right in values)
+			{
+				SignificantNumber expected = Parse((int.Parse(left, CultureInfo.InvariantCulture) * int.Parse(right, CultureInfo.InvariantCulture)).ToString(CultureInfo.InvariantCulture));
+				Assert.AreEqual(expected, Parse(left) * Parse(right), $"{left} * {right}");
+				Assert.AreEqual(Parse(right) * Parse(left), Parse(left) * Parse(right), $"{left} * {right} vs {right} * {left}");
+			}
+		}
+	}
+
+	[TestMethod]
+	[DataRow("0", "1", "0")]
+	[DataRow("0", "-1", "0")]
+	[DataRow("1", "-1", "-1")]
+	[DataRow("-1", "-1", "1")]
+	public void Divide_ExactOperands_ReturnsExactQuotient(string left, string right, string expected) =>
+		Assert.AreEqual(Parse(expected), Parse(left) / Parse(right));
+
+	[TestMethod]
+	[DataRow("0", "1")]
+	[DataRow("1", "1")]
+	[DataRow("-1", "1")]
+	[DataRow("0", "-1")]
+	public void Mod_ExactOperands_ReturnsZero(string left, string right) =>
+		Assert.AreEqual(SignificantNumber.Zero, Parse(left) % Parse(right));
+
+	[TestMethod]
+	public void CompareTo_ExactOperands_IsAntisymmetric()
+	{
+		string[] values = ["-1", "0", "1"];
+		foreach (string left in values)
+		{
+			foreach (string right in values)
+			{
+				int expected = int.Parse(left, CultureInfo.InvariantCulture).CompareTo(int.Parse(right, CultureInfo.InvariantCulture));
+				Assert.AreEqual(expected, int.Sign(Parse(left).CompareTo(Parse(right))), $"{left}.CompareTo({right})");
+			}
+		}
+	}
+
+	[TestMethod]
+	[DataRow("1", "1.23", "1.23")]
+	[DataRow("-1", "1.23", "-1.23")]
+	[DataRow("1.23", "1", "1.23")]
+	[DataRow("1.23", "-1", "-1.23")]
+	[DataRow("0", "1.23", "0")]
+	[DataRow("1.23", "0", "0")]
+	public void Multiply_OneExactOperand_KeepsTheOtherOperandsPrecision(string left, string right, string expected) =>
+		Assert.AreEqual(Parse(expected), Parse(left) * Parse(right));
+
+	[TestMethod]
+	[DataRow("1.23", "1", "1.23")]
+	[DataRow("1.23", "-1", "-1.23")]
+	[DataRow("1", "4.1", "0.24")]
+	public void Divide_OneExactOperand_KeepsTheOtherOperandsPrecision(string left, string right, string expected) =>
+		Assert.AreEqual(Parse(expected), Parse(left) / Parse(right));
+}
diff --git a/SignificantNumber/SignificantNumber.cs b/SignificantNumber/SignificantNumber.cs
index 5ca3bf0..7b43529 100644
--- a/SignificantNumber/SignificantNumber.cs
+++ b/SignificantNumber/SignificantNumber.cs
@@ -178,18 +178,31 @@ private static int LowestDecimalDigits(PreciseNumber left, PreciseNumber right)
 	/// </summary>
 	/// <param name="left">The first number.</param>
 	/// <param name="right">The second number.</param>
-	/// <returns>The lower of the significant digit counts of the two numbers.</returns>
+	/// <returns>
+	/// The lower of the significant digit counts of the two numbers, or 1 when both have unlimited precision, since any
+	/// product, quotient, or remainder of -1, 0, and 1 is exact at one significant digit.
+	/// </returns>
 	private static int LowestSignificantDigits(PreciseNumber left, PreciseNumber right)
 	{
-		int leftSignificantDigits = left.SignificantDigits;
-		int rightSignificantDigits = right.SignificantDigits;
+		bool leftIsExact = HasInfinitePrecision(left);
+		bool rightIsExact = HasInfinitePrecision(right);
+
+		if (leftIsExact && rightIsExact)
+		{
+			return 1;
+		}
 
-		leftSignificantDigits = HasInfinitePrecision(left) ? rightSignificantDigits : leftSignificantDigits;
-		rightSignificantDigits = HasInfinitePrecision(right) ? leftSignificantDigits : rightSignificantDigits;
+		if (leftIsExact)
+		{
+			return right.SignificantDigits;
+		}
+
+		if (rightIsExact)
+		{
+			return left.SignificantDigits;
+		}
 
-		return leftSignificantDigits < rightSignificantDigits
-			? leftSignificantDigits
-			: rightSignificantDigits;
+		return int.Min(left.SignificantDigits, right.SignificantDigits);
 	}
 
 	/// <summary>