diff --git a/Include/floatobject.h b/Include/floatobject.h
index 650d5448ac7..ac510dcd346 100644
--- a/Include/floatobject.h
+++ b/Include/floatobject.h
@@ -111,6 +111,8 @@ PyAPI_FUNC(PyObject *) _PyFloat_FormatAdvanced(PyObject *obj,
 					       Py_UNICODE *format_spec,
 					       Py_ssize_t format_spec_len);
 
+PyAPI_FUNC(PyObject *) _float_to_base(PyObject *v, int base);
+
 #ifdef __cplusplus
 }
 #endif
diff --git a/Lib/test/test_builtin.py b/Lib/test/test_builtin.py
index 7a898b25de4..29c536a2ccd 100644
--- a/Lib/test/test_builtin.py
+++ b/Lib/test/test_builtin.py
@@ -553,6 +553,15 @@ class BuiltinTest(unittest.TestCase):
         self.assertEqual(hex(-16), '-0x10')
         self.assertEqual(hex(-16), '-0x10')
         self.assertRaises(TypeError, hex, {})
+        self.assertEqual(hex(3.125), '0x19 * 2.0 ** -3')
+        self.assertEqual(hex(0.0), '0x0 * 2.0 ** 0')
+        for sv in float('nan'), float('inf'), float('-inf'):
+            self.assertEqual(hex(sv), repr(sv))
+        for i in range(100):
+            x = random.expovariate(.05)
+            self.assertEqual(eval(hex(x)), x, (x, hex(x), eval(hex(x))))
+            self.assertEqual(eval(hex(-x)), -x)
+            self.assertEqual(hex(-x), ('-' + hex(x)))
 
     def test_id(self):
         id(None)
@@ -796,6 +805,15 @@ class BuiltinTest(unittest.TestCase):
         self.assertEqual(oct(-100), '-0o144')
         self.assertEqual(oct(-100), '-0o144')
         self.assertRaises(TypeError, oct, ())
+        self.assertEqual(oct(3.125), '0o31 * 2.0 ** -3')
+        self.assertEqual(oct(0.0), '0o0 * 2.0 ** 0')
+        for sv in float('nan'), float('inf'), float('-inf'):
+            self.assertEqual(oct(sv), repr(sv))
+        for i in range(100):
+            x = random.expovariate(.05)
+            self.assertEqual(eval(oct(x)), x)
+            self.assertEqual(eval(oct(-x)), -x)
+            self.assertEqual(oct(-x), ('-' + oct(x)))
 
     def write_testfile(self):
         # NB the first 4 lines are also used to test input, below
@@ -1213,6 +1231,15 @@ class BuiltinTest(unittest.TestCase):
         self.assertEqual(bin(2**65-1), '0b' + '1' * 65)
         self.assertEqual(bin(-(2**65)), '-0b1' + '0' * 65)
         self.assertEqual(bin(-(2**65-1)), '-0b' + '1' * 65)
+        self.assertEqual(bin(3.125), '0b11001 * 2.0 ** -3')
+        self.assertEqual(bin(0.0), '0b0 * 2.0 ** 0')
+        for sv in float('nan'), float('inf'), float('-inf'):
+            self.assertEqual(bin(sv), repr(sv))
+        for i in range(100):
+            x = random.expovariate(.05)
+            self.assertEqual(eval(bin(x)), x)
+            self.assertEqual(eval(bin(-x)), -x)
+            self.assertEqual(bin(-x), ('-' + bin(x)))
 
 class TestSorted(unittest.TestCase):
 
diff --git a/Objects/abstract.c b/Objects/abstract.c
index 60a5e849cfd..0d40d17d659 100644
--- a/Objects/abstract.c
+++ b/Objects/abstract.c
@@ -1451,8 +1451,11 @@ PyObject *
 PyNumber_ToBase(PyObject *n, int base)
 {
 	PyObject *res = NULL;
-	PyObject *index = PyNumber_Index(n);
+	PyObject *index;
 
+	if (PyFloat_Check(n))
+		return _float_to_base(n, base);
+	index = PyNumber_Index(n);
 	if (!index)
 		return NULL;
 	if (PyLong_Check(index))
diff --git a/Objects/floatobject.c b/Objects/floatobject.c
index db1c99f687e..2465fa959a3 100644
--- a/Objects/floatobject.c
+++ b/Objects/floatobject.c
@@ -1113,6 +1113,36 @@ PyDoc_STRVAR(float_as_integer_ratio_doc,
 ">>> (-.25).as_integer_ratio()\n"
 "(-1, 4)");
 
+PyObject *
+_float_to_base(PyObject *v, int base)
+{
+	PyObject *mant, *conv, *result;
+	double x, fr;
+	int i, exp;
+
+	if (!PyFloat_Check(v)) {
+		PyErr_BadInternalCall();
+		return NULL;
+	}
+	CONVERT_TO_DOUBLE(v, x);
+	if (!Py_IS_FINITE(x))
+		return PyObject_Repr(v);
+	fr = frexp(x, &exp);
+	for (i=0; i<300 && fr != floor(fr) ; i++) {
+		fr *= 2.0;
+		exp--;
+	}
+	mant = PyLong_FromDouble(floor(fr));
+	if (mant == NULL)
+		return NULL;
+	conv = PyNumber_ToBase(mant, base);
+	Py_DECREF(mant);
+	if (conv == NULL)
+		return NULL;
+	result = PyUnicode_FromFormat("%U * 2.0 ** %d", conv, exp);
+	Py_DECREF(conv);
+	return result;
+}
 
 static PyObject *
 float_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds);