diff --git a/numpy/core/src/multiarray/convert_datatype.c b/numpy/core/src/multiarray/convert_datatype.c
index 7f31fd656d22..627784db3e23 100644
--- a/numpy/core/src/multiarray/convert_datatype.c
+++ b/numpy/core/src/multiarray/convert_datatype.c
@@ -2881,7 +2881,7 @@ add_other_to_and_from_string_cast(
         .name = "legacy_cast_to_string",
         .nin = 1,
         .nout = 1,
-        .flags = NPY_METH_REQUIRES_PYAPI,
+        .flags = NPY_METH_REQUIRES_PYAPI | NPY_METH_NO_FLOATINGPOINT_ERRORS,
         .dtypes = dtypes,
         .slots = slots,
     };
diff --git a/numpy/core/src/multiarray/scalartypes.c.src b/numpy/core/src/multiarray/scalartypes.c.src
index 8f0b694d22fe..2d3abadd26ee 100644
--- a/numpy/core/src/multiarray/scalartypes.c.src
+++ b/numpy/core/src/multiarray/scalartypes.c.src
@@ -896,15 +896,21 @@ static PyObject *
 @name@type_@kind@_either(npy_@name@ val, TrimMode trim_pos, TrimMode trim_sci,
                          npy_bool sign)
 {
-    npy_@name@ absval;
 
     if (npy_legacy_print_mode <= 113) {
         return legacy_@name@_format@kind@(val);
     }
 
-    absval = val < 0 ? -val : val;
+    int use_positional;
+    if (npy_isnan(val) || val == 0) {
+         use_positional = 1;
+    }
+    else {
+        npy_@name@ absval = val < 0 ? -val : val;
+        use_positional = absval < 1.e16L && absval >= 1.e-4L;
+    }
 
-    if (absval == 0 || (absval < 1.e16L && absval >= 1.e-4L) ) {
+    if (use_positional) {
         return format_@name@(val, 0, -1, sign, trim_pos, -1, -1, -1);
     }
     return format_@name@(val, 1, -1, sign, trim_sci, -1, -1, -1);
diff --git a/numpy/core/tests/test_strings.py b/numpy/core/tests/test_strings.py
index 2b87ed654a0b..42f775e857b8 100644
--- a/numpy/core/tests/test_strings.py
+++ b/numpy/core/tests/test_strings.py
@@ -83,3 +83,17 @@ def test_string_comparisons_empty(op, ufunc, sym, dtypes):
     assert_array_equal(op(arr, arr2), expected)
     assert_array_equal(ufunc(arr, arr2), expected)
     assert_array_equal(np.compare_chararrays(arr, arr2, sym, False), expected)
+
+
+@pytest.mark.parametrize("str_dt", ["S", "U"])
+@pytest.mark.parametrize("float_dt", np.typecodes["AllFloat"])
+def test_float_to_string_cast(str_dt, float_dt):
+    float_dt = np.dtype(float_dt)
+    fi = np.finfo(float_dt)
+    arr = np.array([np.nan, np.inf, -np.inf, fi.max, fi.min], dtype=float_dt)
+    expected = ["nan", "inf", "-inf", repr(fi.max), repr(fi.min)]
+    if float_dt.kind == 'c':
+        expected = [f"({r}+0j)" for r in expected]
+
+    res = arr.astype(str_dt)
+    assert_array_equal(res, np.array(expected, dtype=str_dt))