diff --git a/astropy/io/fits/card.py b/astropy/io/fits/card.py
index 118bfced89e8..c3197b92041d 100644
--- a/astropy/io/fits/card.py
+++ b/astropy/io/fits/card.py
@@ -1297,35 +1297,90 @@ def _format_value(value):
         return ""
 
 
-def _format_float(value):
-    """Format a floating number to make sure it gets the decimal point."""
-    value_str = f"{value:.16G}"
-    if "." not in value_str and "E" not in value_str:
-        value_str += ".0"
-    elif "E" in value_str:
-        # On some Windows builds of Python (and possibly other platforms?) the
-        # exponent is zero-padded out to, it seems, three digits.  Normalize
-        # the format to pad only to two digits.
-        significand, exponent = value_str.split("E")
-        if exponent[0] in ("+", "-"):
-            sign = exponent[0]
-            exponent = exponent[1:]
-        else:
-            sign = ""
-        value_str = f"{significand}E{sign}{int(exponent):02d}"
-
-    # Limit the value string to at most 20 characters.
-    str_len = len(value_str)
-
-    if str_len > 20:
-        idx = value_str.find("E")
+def _normalize_float_str(s):
+    """
+    Normalize a float string for FITS:
+    - Uppercase exponent letter to 'E'
+    - Exponent normalization: include a sign and at least two digits only
+      if abs(exponent) < 100; otherwise preserve full width without extra
+      padding zeros.
+    - Ensure integer-like floats include a decimal point (e.g., '2.0').
+    """
+    # Do not alter special floats
+    sl = s.lower()
+    if sl in ("nan", "inf", "-inf"):
+        return s
 
-        if idx < 0:
-            value_str = value_str[:20]
+    # Normalize exponent
+    if "e" in s or "E" in s:
+        s = s.replace("e", "E")
+        mant, exp = s.split("E", 1)
+        # Remove spaces in exponent part and ensure a sign
+        exp = exp.replace(" ", "")
+        if not exp or exp[0] not in "+-":
+            exp = "+" + exp
+        # Parse exponent as integer
+        try:
+            exp_int = int(exp)
+        except ValueError:
+            # Fallback: strip sign and parse digits only
+            sign_char = exp[0] if exp and exp[0] in "+-" else "+"
+            digits = exp[1:]
+            try:
+                exp_int = int(("-" if sign_char == "-" else "") + (digits or "0"))
+            except ValueError:
+                exp_int = 0
+        sign_char = "+" if exp_int >= 0 else "-"
+        abs_exp = abs(exp_int)
+        if abs_exp < 100:
+            digits_out = f"{abs_exp:02d}"
         else:
-            value_str = value_str[: 20 - (str_len - idx)] + value_str[idx:]
+            digits_out = str(abs_exp)
+        s = mant + "E" + sign_char + digits_out
+    # Ensure integer-like floats include a decimal point
+    if ("E" not in s) and ("." not in s):
+        s = s + ".0"
+    return s
 
-    return value_str
+def _format_float(value):
+    """
+    Format a float according to FITS card value rules:
+    - Prefer Python's minimal round-trip representation (str(value)) when it fits
+      within the 20-character numeric field; otherwise use scientific notation
+      with precision-based rounding.
+    - Exponent is normalized (uppercase 'E', sign, and at least two digits
+      only for abs(exp) < 100; otherwise preserve full width).
+    - Ensure integer-like floats include a decimal point.
+    - Special floats (NaN/Inf) behavior unchanged.
+    """
+    # Primary candidate: minimal round-trip representation
+    try:
+        s1 = str(value)
+    except Exception:
+        s1 = f"{value:.16G}"
+    sl = s1.lower()
+    # Preserve special float behavior unchanged
+    if sl in ("nan", "inf", "-inf"):
+        return s1
+    s1n = _normalize_float_str(s1)
+    if len(s1n) <= 20:
+        return s1n
+
+    # Use scientific notation with precision-based rounding
+    # Start with up to 16 digits after decimal and reduce until it fits
+    N = 16
+    while N >= 0:
+        sci = f"{value:.{N}E}"
+        sci_n = _normalize_float_str(sci)
+        if len(sci_n) <= 20:
+            return sci_n
+        N -= 1
+
+    # Fallback: if somehow still too long, take normalized minimal and truncate
+    out = s1n[:20]
+    if out.endswith("."):
+        out = out[:-1] or "0"
+    return out
 
 
 def _pad(input):
diff --git a/astropy/io/fits/tests/test_float_format.py b/astropy/io/fits/tests/test_float_format.py
new file mode 100644
index 000000000000..3d9bf23a8fed
--- /dev/null
+++ b/astropy/io/fits/tests/test_float_format.py
@@ -0,0 +1,102 @@
+import pytest
+from astropy.io import fits
+from astropy.io.fits.verify import VerifyWarning
+
+
+def _value_field(card_str):
+    """
+    Extract the fixed-width value field (up to 20 characters) after '='.
+    For standard FITS cards, the numeric value field is exactly 20 characters
+    and right-justified after '= '. HIERARCH cards may omit the space or use
+    a shortened value indicator; this helper is intended for standard cards
+    in these tests.
+    """
+    if '=' not in card_str:
+        return ''
+    eq = card_str.index('=')
+    # After '=' there is typically a space before the field
+    start = eq + 1
+    if start < len(card_str) and card_str[start] == ' ':
+        start += 1
+    end = min(start + 20, len(card_str))
+    return card_str[start:end]
+
+
+def test_hierarch_float_minimal_repr_no_truncate():
+    c = fits.Card(
+        'HIERARCH ESO IFM CL RADIUS',
+        0.009125,
+        '[m] radius arround actuator to avoid'
+    )
+    with pytest.warns(None) as rec:
+        s = str(c)
+    # No VerifyWarning
+    assert not any(isinstance(w.message, VerifyWarning) for w in rec)
+    # Card is exactly 80 chars
+    assert len(s) == 80
+    # Value uses minimal representation and comment preserved
+    assert '= 0.009125 /' in s
+    assert s.endswith('[m] radius arround actuator to avoid')
+
+
+def test_float_minimal_repr_exponent_uppercase():
+    c = fits.Card('FOO', 1e-5)
+    s = str(c)
+    # Uppercase exponent with two digits
+    assert 'E-05' in s
+    # Value field is right-justified within 20 chars for standard card
+    vf = _value_field(s)
+    assert len(vf) == 20
+    assert vf.endswith('E-05')
+    # Leading spaces indicate right-justification
+    assert vf[0] == ' '
+
+
+def test_float_integer_like_has_decimal_point():
+    c = fits.Card('BAR', 2.0)
+    s = str(c)
+    vf = _value_field(s)
+    assert '2.0' in vf
+
+
+def test_complex_minimal_repr():
+    c = fits.Card('BAZ', complex(0.009125, -5e-6))
+    s = str(c)
+    # Real part minimal, imag part uses normalized small exponent
+    assert '0.009125' in s
+    assert 'E-06' in s
+    vf = _value_field(s)
+    # Entire complex literal should fit in the 20-char field in standard cards
+    assert len(vf) <= 20
+
+
+def test_hierarch_equal_sign_shortening():
+    # Construct a HIERARCH card near the limit to force '='-shortening logic
+    # The specific keyword and value combo aims to exceed by 1 char before shortening
+    key = 'HIERARCH ESO VERY LONG KEYWORD TEST'
+    comment = 'C' * 30
+    c = fits.Card(key, 0.009125, comment)
+    with pytest.warns(None) as rec:
+        s = str(c)
+    # Shortening occurs without raising errors; card length should be 80
+    assert len(s) == 80
+    # No VerifyWarning
+    assert not any(isinstance(w.message, VerifyWarning) for w in rec)
+
+
+def test_negative_zero_preserved():
+    c = fits.Card('NEGZERO', -0.0)
+    s = str(c)
+    vf = _value_field(s)
+    # Ensure the sign and decimal point are preserved for -0.0
+    assert '-0.0' in vf
+
+
+def test_large_exponent_not_zero_padded():
+    c = fits.Card('BIG', 1e100)
+    s = str(c)
+    vf = _value_field(s)
+    # Exponent should be normalized with uppercase E, explicit sign, and
+    # no forced zero-padding beyond the natural width (E+100 here)
+    assert 'E+100' in vf
+    assert len(vf) <= 20