diff --git a/library/core/src/num/flt2dec/strategy/dragon.rs b/library/core/src/num/flt2dec/strategy/dragon.rs
index 8ced5971ec2f9..71b14d0ae3f4c 100644
--- a/library/core/src/num/flt2dec/strategy/dragon.rs
+++ b/library/core/src/num/flt2dec/strategy/dragon.rs
@@ -366,7 +366,7 @@ pub fn format_exact<'a>(
     if order == Ordering::Greater
         || (order == Ordering::Equal
             // SAFETY: `buf[len-1]` is initialized.
-            && (len == 0 || unsafe { buf[len - 1].assume_init() } & 1 == 1))
+            && len > 0 && unsafe { buf[len - 1].assume_init() } & 1 == 1)
     {
         // if rounding up changes the length, the exponent should also change.
         // but we've been requested a fixed number of digits, so do not alter the buffer...
diff --git a/library/core/tests/fmt/float.rs b/library/core/tests/fmt/float.rs
index 47a7400f76ef9..003782f34dc93 100644
--- a/library/core/tests/fmt/float.rs
+++ b/library/core/tests/fmt/float.rs
@@ -5,7 +5,7 @@ fn test_format_f64() {
     assert_eq!("10", format!("{:.0}", 9.9f64));
     assert_eq!("9.8", format!("{:.1}", 9.849f64));
     assert_eq!("9.9", format!("{:.1}", 9.851f64));
-    assert_eq!("1", format!("{:.0}", 0.5f64));
+    assert_eq!("0", format!("{:.0}", 0.5f64));
     assert_eq!("1.23456789e6", format!("{:e}", 1234567.89f64));
     assert_eq!("1.23456789e3", format!("{:e}", 1234.56789f64));
     assert_eq!("1.23456789E6", format!("{:E}", 1234567.89f64));
@@ -24,6 +24,66 @@ fn test_format_f64() {
     assert_eq!("1234.6", format!("{:.1?}", 1234.56789f64));
 }
 
+#[test]
+fn test_format_f64_rounds_ties_to_even() {
+    assert_eq!("0", format!("{:.0}", 0.5f64));
+    assert_eq!("2", format!("{:.0}", 1.5f64));
+    assert_eq!("2", format!("{:.0}", 2.5f64));
+    assert_eq!("4", format!("{:.0}", 3.5f64));
+    assert_eq!("4", format!("{:.0}", 4.5f64));
+    assert_eq!("6", format!("{:.0}", 5.5f64));
+    assert_eq!("128", format!("{:.0}", 127.5f64));
+    assert_eq!("128", format!("{:.0}", 128.5f64));
+    assert_eq!("0.2", format!("{:.1}", 0.25f64));
+    assert_eq!("0.8", format!("{:.1}", 0.75f64));
+    assert_eq!("0.12", format!("{:.2}", 0.125f64));
+    assert_eq!("0.88", format!("{:.2}", 0.875f64));
+    assert_eq!("0.062", format!("{:.3}", 0.062f64));
+    assert_eq!("-0", format!("{:.0}", -0.5f64));
+    assert_eq!("-2", format!("{:.0}", -1.5f64));
+    assert_eq!("-2", format!("{:.0}", -2.5f64));
+    assert_eq!("-4", format!("{:.0}", -3.5f64));
+    assert_eq!("-4", format!("{:.0}", -4.5f64));
+    assert_eq!("-6", format!("{:.0}", -5.5f64));
+    assert_eq!("-128", format!("{:.0}", -127.5f64));
+    assert_eq!("-128", format!("{:.0}", -128.5f64));
+    assert_eq!("-0.2", format!("{:.1}", -0.25f64));
+    assert_eq!("-0.8", format!("{:.1}", -0.75f64));
+    assert_eq!("-0.12", format!("{:.2}", -0.125f64));
+    assert_eq!("-0.88", format!("{:.2}", -0.875f64));
+    assert_eq!("-0.062", format!("{:.3}", -0.062f64));
+
+    assert_eq!("2e0", format!("{:.0e}", 1.5f64));
+    assert_eq!("2e0", format!("{:.0e}", 2.5f64));
+    assert_eq!("4e0", format!("{:.0e}", 3.5f64));
+    assert_eq!("4e0", format!("{:.0e}", 4.5f64));
+    assert_eq!("6e0", format!("{:.0e}", 5.5f64));
+    assert_eq!("1.28e2", format!("{:.2e}", 127.5f64));
+    assert_eq!("1.28e2", format!("{:.2e}", 128.5f64));
+    assert_eq!("-2e0", format!("{:.0e}", -1.5f64));
+    assert_eq!("-2e0", format!("{:.0e}", -2.5f64));
+    assert_eq!("-4e0", format!("{:.0e}", -3.5f64));
+    assert_eq!("-4e0", format!("{:.0e}", -4.5f64));
+    assert_eq!("-6e0", format!("{:.0e}", -5.5f64));
+    assert_eq!("-1.28e2", format!("{:.2e}", -127.5f64));
+    assert_eq!("-1.28e2", format!("{:.2e}", -128.5f64));
+
+    assert_eq!("2E0", format!("{:.0E}", 1.5f64));
+    assert_eq!("2E0", format!("{:.0E}", 2.5f64));
+    assert_eq!("4E0", format!("{:.0E}", 3.5f64));
+    assert_eq!("4E0", format!("{:.0E}", 4.5f64));
+    assert_eq!("6E0", format!("{:.0E}", 5.5f64));
+    assert_eq!("1.28E2", format!("{:.2E}", 127.5f64));
+    assert_eq!("1.28E2", format!("{:.2E}", 128.5f64));
+    assert_eq!("-2E0", format!("{:.0E}", -1.5f64));
+    assert_eq!("-2E0", format!("{:.0E}", -2.5f64));
+    assert_eq!("-4E0", format!("{:.0E}", -3.5f64));
+    assert_eq!("-4E0", format!("{:.0E}", -4.5f64));
+    assert_eq!("-6E0", format!("{:.0E}", -5.5f64));
+    assert_eq!("-1.28E2", format!("{:.2E}", -127.5f64));
+    assert_eq!("-1.28E2", format!("{:.2E}", -128.5f64));
+}
+
 #[test]
 fn test_format_f32() {
     assert_eq!("1", format!("{:.0}", 1.0f32));
@@ -31,7 +91,7 @@ fn test_format_f32() {
     assert_eq!("10", format!("{:.0}", 9.9f32));
     assert_eq!("9.8", format!("{:.1}", 9.849f32));
     assert_eq!("9.9", format!("{:.1}", 9.851f32));
-    assert_eq!("1", format!("{:.0}", 0.5f32));
+    assert_eq!("0", format!("{:.0}", 0.5f32));
     assert_eq!("1.2345679e6", format!("{:e}", 1234567.89f32));
     assert_eq!("1.2345679e3", format!("{:e}", 1234.56789f32));
     assert_eq!("1.2345679E6", format!("{:E}", 1234567.89f32));
@@ -50,6 +110,66 @@ fn test_format_f32() {
     assert_eq!("1234.6", format!("{:.1?}", 1234.56789f32));
 }
 
+#[test]
+fn test_format_f32_rounds_ties_to_even() {
+    assert_eq!("0", format!("{:.0}", 0.5f32));
+    assert_eq!("2", format!("{:.0}", 1.5f32));
+    assert_eq!("2", format!("{:.0}", 2.5f32));
+    assert_eq!("4", format!("{:.0}", 3.5f32));
+    assert_eq!("4", format!("{:.0}", 4.5f32));
+    assert_eq!("6", format!("{:.0}", 5.5f32));
+    assert_eq!("128", format!("{:.0}", 127.5f32));
+    assert_eq!("128", format!("{:.0}", 128.5f32));
+    assert_eq!("0.2", format!("{:.1}", 0.25f32));
+    assert_eq!("0.8", format!("{:.1}", 0.75f32));
+    assert_eq!("0.12", format!("{:.2}", 0.125f32));
+    assert_eq!("0.88", format!("{:.2}", 0.875f32));
+    assert_eq!("0.062", format!("{:.3}", 0.062f32));
+    assert_eq!("-0", format!("{:.0}", -0.5f32));
+    assert_eq!("-2", format!("{:.0}", -1.5f32));
+    assert_eq!("-2", format!("{:.0}", -2.5f32));
+    assert_eq!("-4", format!("{:.0}", -3.5f32));
+    assert_eq!("-4", format!("{:.0}", -4.5f32));
+    assert_eq!("-6", format!("{:.0}", -5.5f32));
+    assert_eq!("-128", format!("{:.0}", -127.5f32));
+    assert_eq!("-128", format!("{:.0}", -128.5f32));
+    assert_eq!("-0.2", format!("{:.1}", -0.25f32));
+    assert_eq!("-0.8", format!("{:.1}", -0.75f32));
+    assert_eq!("-0.12", format!("{:.2}", -0.125f32));
+    assert_eq!("-0.88", format!("{:.2}", -0.875f32));
+    assert_eq!("-0.062", format!("{:.3}", -0.062f32));
+
+    assert_eq!("2e0", format!("{:.0e}", 1.5f32));
+    assert_eq!("2e0", format!("{:.0e}", 2.5f32));
+    assert_eq!("4e0", format!("{:.0e}", 3.5f32));
+    assert_eq!("4e0", format!("{:.0e}", 4.5f32));
+    assert_eq!("6e0", format!("{:.0e}", 5.5f32));
+    assert_eq!("1.28e2", format!("{:.2e}", 127.5f32));
+    assert_eq!("1.28e2", format!("{:.2e}", 128.5f32));
+    assert_eq!("-2e0", format!("{:.0e}", -1.5f32));
+    assert_eq!("-2e0", format!("{:.0e}", -2.5f32));
+    assert_eq!("-4e0", format!("{:.0e}", -3.5f32));
+    assert_eq!("-4e0", format!("{:.0e}", -4.5f32));
+    assert_eq!("-6e0", format!("{:.0e}", -5.5f32));
+    assert_eq!("-1.28e2", format!("{:.2e}", -127.5f32));
+    assert_eq!("-1.28e2", format!("{:.2e}", -128.5f32));
+
+    assert_eq!("2E0", format!("{:.0E}", 1.5f32));
+    assert_eq!("2E0", format!("{:.0E}", 2.5f32));
+    assert_eq!("4E0", format!("{:.0E}", 3.5f32));
+    assert_eq!("4E0", format!("{:.0E}", 4.5f32));
+    assert_eq!("6E0", format!("{:.0E}", 5.5f32));
+    assert_eq!("1.28E2", format!("{:.2E}", 127.5f32));
+    assert_eq!("1.28E2", format!("{:.2E}", 128.5f32));
+    assert_eq!("-2E0", format!("{:.0E}", -1.5f32));
+    assert_eq!("-2E0", format!("{:.0E}", -2.5f32));
+    assert_eq!("-4E0", format!("{:.0E}", -3.5f32));
+    assert_eq!("-4E0", format!("{:.0E}", -4.5f32));
+    assert_eq!("-6E0", format!("{:.0E}", -5.5f32));
+    assert_eq!("-1.28E2", format!("{:.2E}", -127.5f32));
+    assert_eq!("-1.28E2", format!("{:.2E}", -128.5f32));
+}
+
 fn is_exponential(s: &str) -> bool {
     s.contains("e") || s.contains("E")
 }
diff --git a/library/core/tests/num/flt2dec/mod.rs b/library/core/tests/num/flt2dec/mod.rs
index 798473bbde377..30843cc3dd79c 100644
--- a/library/core/tests/num/flt2dec/mod.rs
+++ b/library/core/tests/num/flt2dec/mod.rs
@@ -138,7 +138,7 @@ where
 
     // check exact rounding for zero- and negative-width cases
     let start;
-    if expected[0] >= b'5' {
+    if expected[0] > b'5' {
         try_fixed!(f(&decoded) => &mut buf, expectedk, b"1", expectedk + 1;
                    "zero-width rounding-up mismatch for v={v}: \
                     actual {actual:?}, expected {expected:?}",
@@ -1007,7 +1007,7 @@ where
     assert_eq!(to_string(f, 999.5, Minus, 3), "999.500");
     assert_eq!(to_string(f, 999.5, Minus, 30), "999.500000000000000000000000000000");
 
-    assert_eq!(to_string(f, 0.5, Minus, 0), "1");
+    assert_eq!(to_string(f, 0.5, Minus, 0), "0");
     assert_eq!(to_string(f, 0.5, Minus, 1), "0.5");
     assert_eq!(to_string(f, 0.5, Minus, 2), "0.50");
     assert_eq!(to_string(f, 0.5, Minus, 3), "0.500");