diff --git a/PreciseNumber.Test/PreciseNumberParseTrailingNulTests.cs b/PreciseNumber.Test/PreciseNumberParseTrailingNulTests.cs
index 7fce253..37d054d 100644
--- a/PreciseNumber.Test/PreciseNumberParseTrailingNulTests.cs
+++ b/PreciseNumber.Test/PreciseNumberParseTrailingNulTests.cs
@@ -19,6 +19,8 @@ public class PreciseNumberParseTrailingNulTests
 	[DataRow("1e3 \0", NumberStyles.Float)]
 	[DataRow("12345\0\0\0\0\0\0\0\0", NumberStyles.Integer)]
 	[DataRow("-0.25\0", NumberStyles.Number)]
+	[DataRow("3e1\0", NumberStyles.Float)]
+	[DataRow("3e1\0\0", NumberStyles.Float)]
 	public void ParseIgnoresTrailingNulsAsDecimalDoes(string text, NumberStyles style)
 	{
 		CultureInfo culture = CultureInfo.InvariantCulture;
@@ -51,4 +53,23 @@ public void ParseStillRejectsNulsThatAreNotTheLastCharacters(string text, Number
 		Assert.IsFalse(PreciseNumber.TryParse(text.AsSpan(), style, culture, out _));
 		Assert.ThrowsExactly<FormatException>(() => PreciseNumber.Parse(text, style, culture));
 	}
+
+	[TestMethod]
+	[DataRow("3e1\0 ", NumberStyles.Float)]
+	[DataRow("3E0\0 ", NumberStyles.Any)]
+	[DataRow("3e1\0-", NumberStyles.Any)]
+	[DataRow("3e1\0\0-", NumberStyles.Any)]
+	[DataRow("3e1\0$", NumberStyles.Any)]
+	public void ParseRejectsANulInsideTheExponent(string text, NumberStyles style)
+	{
+		// Invariant, but with en-US's currency symbol, so "$" is read as one.
+		NumberFormatInfo culture = (NumberFormatInfo)NumberFormatInfo.InvariantInfo.Clone();
+		culture.CurrencySymbol = "$";
+		Assert.IsFalse(decimal.TryParse(text, style, culture, out _), "The case must be one decimal rejects.");
+		Assert.IsFalse(double.TryParse(text, style, culture, out _), "The case must be one double rejects.");
+
+		Assert.IsFalse(PreciseNumber.TryParse(text, style, culture, out _));
+		Assert.IsFalse(PreciseNumber.TryParse(text.AsSpan(), style, culture, out _));
+		Assert.ThrowsExactly<FormatException>(() => PreciseNumber.Parse(text, style, culture));
+	}
 }
diff --git a/PreciseNumber/PreciseNumber.cs b/PreciseNumber/PreciseNumber.cs
index 8d5ec22..6191744 100644
--- a/PreciseNumber/PreciseNumber.cs
+++ b/PreciseNumber/PreciseNumber.cs
@@ -1409,6 +1409,13 @@ private static PreciseNumber FromParsedParts(ReadOnlySpan<char> digits, int deci
 		long exponent = 0;
 		if (hasExponent)
 		{
+			// long.Parse ignores trailing NULs by itself, so a NUL the parse kept because something follows
+			// it, as in "3e1\0 " once the white space is trimmed, would otherwise slip through here.
+			if (exponentText.Contains('\0'))
+			{
+				throw new FormatException(InvalidFormatMessage);
+			}
+
 			// Only a sign may precede its digits: NumberStyles.Integer would also let white space through,
 			// accepting "1e 5" where every BCL numeric type rejects it. A zero is zero whatever its written
 			// exponent, as for decimal and double, so only a nonzero value can overflow here.