diff --git a/Lib/test/test_builtin.py b/Lib/test/test_builtin.py
index a11e40aa15b..54df9e114d0 100644
--- a/Lib/test/test_builtin.py
+++ b/Lib/test/test_builtin.py
@@ -608,8 +608,7 @@ def test_float(self):
         if have_unicode:
             self.assertEqual(float(str("  3.14  ")), 3.14)
             self.assertEqual(float(str(b"  \u0663.\u0661\u0664  ",'raw-unicode-escape')), 3.14)
-            # Implementation limitation in PyFloat_FromString()
-            self.assertRaises(ValueError, float, str("1"*10000))
+            self.assertEqual(float("1"*10000), 1e10000) # Inf on both sides
 
     @run_with_locale('LC_NUMERIC', 'fr_FR', 'de_DE')
     def test_float_with_comma(self):
diff --git a/Python/bltinmodule.c b/Python/bltinmodule.c
index aa0d0df1a28..064b92a7bd4 100644
--- a/Python/bltinmodule.c
+++ b/Python/bltinmodule.c
@@ -1230,7 +1230,7 @@ builtin_hex(PyObject *self, PyObject *v)
 		return NULL;
 	}
 	res = (*nb->nb_hex)(v);
-	if (res && !PyString_Check(res)) {
+	if (res && !PyString_Check(res) && !PyUnicode_Check(res)) {
 		PyErr_Format(PyExc_TypeError,
 			     "__hex__ returned non-string (type %.200s)",
 			     res->ob_type->tp_name);
@@ -1430,7 +1430,7 @@ builtin_oct(PyObject *self, PyObject *v)
 		return NULL;
 	}
 	res = (*nb->nb_oct)(v);
-	if (res && !PyString_Check(res)) {
+	if (res && !PyString_Check(res) && !PyUnicode_Check(res)) {
 		PyErr_Format(PyExc_TypeError,
 			     "__oct__ returned non-string (type %.200s)",
 			     res->ob_type->tp_name);