diff --git a/Tests/test_file_tiff_metadata.py b/Tests/test_file_tiff_metadata.py
index 36ad8cee9..67b05b895 100644
--- a/Tests/test_file_tiff_metadata.py
+++ b/Tests/test_file_tiff_metadata.py
@@ -1,6 +1,7 @@
 from __future__ import annotations
 
 import io
+import math
 import struct
 from pathlib import Path
 
@@ -280,6 +281,30 @@ def test_writing_other_types_to_undefined(
         assert reloaded.tag_v2[33723] == b"1"
 
 
+@pytest.mark.parametrize(
+    "value, expected",
+    (
+        (IFDRational(1, 0), TiffTags.RATIONAL),
+        (IFDRational(-1, 0), TiffTags.SIGNED_RATIONAL),
+    ),
+)
+def test_tagtype_on_zero_denominator(
+    value: IFDRational, expected: int, tmp_path: Path
+) -> None:
+    info = TiffImagePlugin.ImageFileDirectory_v2()
+
+    info[37380] = value
+    assert info.tagtype[37380] == expected
+
+    im = hopper()
+    out = tmp_path / "temp.tiff"
+    im.save(out, tiffinfo=info)
+
+    with Image.open(out) as reloaded:
+        assert isinstance(reloaded, TiffImagePlugin.TiffImageFile)
+        assert math.isnan(reloaded.tag_v2[37380])
+
+
 def test_undefined_zero(tmp_path: Path) -> None:
     # Check that the tag has not been changed since this test was created
     tag = TiffTags.TAGS_V2[45059]
diff --git a/Tests/test_tiff_ifdrational.py b/Tests/test_tiff_ifdrational.py
index 42d06b896..8aae609a5 100644
--- a/Tests/test_tiff_ifdrational.py
+++ b/Tests/test_tiff_ifdrational.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+import math
 from fractions import Fraction
 from pathlib import Path
 
@@ -74,3 +75,18 @@ def test_ifd_rational_save(
     with Image.open(out) as reloaded:
         assert isinstance(reloaded, TiffImagePlugin.TiffImageFile)
         assert float(IFDRational(301, 1)) == float(reloaded.tag_v2[282])
+
+
+@pytest.mark.parametrize(
+    "numerator, denominator, expected_result",
+    [
+        (1, 1, 1.0),
+        (1, 0, float("nan")),
+    ],
+)
+def test_float_cast(numerator: int, denominator: int, expected_result: float) -> None:
+    value = float(IFDRational(numerator, denominator))
+    if math.isnan(expected_result):
+        assert value
+    else:
+        assert value == expected_result
diff --git a/src/PIL/TiffImagePlugin.py b/src/PIL/TiffImagePlugin.py
index c1850f084..29e9f7731 100644
--- a/src/PIL/TiffImagePlugin.py
+++ b/src/PIL/TiffImagePlugin.py
@@ -398,6 +398,9 @@ class IFDRational(Rational):
         f = self._val.limit_denominator(max_denominator)
         return f.numerator, f.denominator
 
+    def __float__(self) -> float:
+        return float(self._val)
+
     def __repr__(self) -> str:
         return str(float(self._val))
 
@@ -684,7 +687,7 @@ class ImageFileDirectory_v2(_IFDv2Base):
                 if all(isinstance(v, IFDRational) for v in values):
                     for v in values:
                         assert isinstance(v, IFDRational)
-                        if v < 0:
+                        if v < 0 or (math.isnan(v) and float(v.numerator) < 0):
                             self.tagtype[tag] = TiffTags.SIGNED_RATIONAL
                             break
                     else: