diff --git a/Lib/test/test_builtin.py b/Lib/test/test_builtin.py
index 15d80a36983..8c46ab8eb3f 100644
--- a/Lib/test/test_builtin.py
+++ b/Lib/test/test_builtin.py
@@ -631,6 +631,15 @@ class BuiltinTest(unittest.TestCase):
         self.assertEqual(hex(-16), '-0x10')
         self.assertEqual(hex(-16L), '-0x10L')
         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)
@@ -914,6 +923,15 @@ class BuiltinTest(unittest.TestCase):
         self.assertEqual(oct(-100), '-0144')
         self.assertEqual(oct(-100L), '-0144L')
         self.assertRaises(TypeError, oct, ())
+        self.assertEqual(oct(3.125), '031 * 2.0 ** -3')
+        self.assertEqual(oct(0.0), '0 * 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 and raw_input, below
@@ -1466,6 +1484,15 @@ 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/Misc/NEWS b/Misc/NEWS
index 96d45af0880..2825198169d 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -17,6 +17,9 @@ Core and Builtins
   slice(None, 10, -1).indices(10) returns (9, 9, -1) instead of (9,
   10, -1).
 
+- Issue 3008: hex(), oct(), and bin() can now create exact reprs 
+  for floats.
+
 - Make bin() implementation parallel oct() and hex().
 
 
diff --git a/Objects/floatobject.c b/Objects/floatobject.c
index 32e7cc8088c..bbe8a196162 100644
--- a/Objects/floatobject.c
+++ b/Objects/floatobject.c
@@ -1204,6 +1204,62 @@ PyDoc_STRVAR(float_as_integer_ratio_doc,
 ">>> (-.25).as_integer_ratio()\n"
 "(-1, 4)");
 
+static PyObject *
+_float_to_base(PyFloatObject *v, unaryfunc int_to_base)
+{
+	PyObject *mant, *conv, *result;
+	double x, fr;
+	int i, exp, n;
+	char *conv_str;
+
+	CONVERT_TO_DOUBLE(((PyObject *)v), x);
+	if (!Py_IS_FINITE(x))
+		return PyObject_Repr((PyObject *)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 = int_to_base(mant);
+	Py_DECREF(mant);
+	if (conv== NULL)
+		return NULL;
+	n = PyString_GET_SIZE(conv);
+	conv_str = PyString_AS_STRING(conv);
+	/* Remove the trailing 'L' if present */
+	if (n && conv_str[n-1] == 'L') {
+		PyObject *newconv = PySequence_GetSlice(conv, 0, -1);
+		Py_DECREF(conv);
+		if (newconv == NULL)
+			return NULL;
+		conv = newconv;
+		conv_str = PyString_AS_STRING(conv);
+	}
+	result = PyString_FromFormat("%s * 2.0 ** %d", conv_str, exp);
+	Py_DECREF(conv);
+	return result;
+}
+
+static PyObject *
+float_hex(PyFloatObject *v)
+{
+	return _float_to_base(v, PyLong_Type.tp_as_number->nb_hex);
+}
+
+static PyObject *
+float_oct(PyFloatObject *v)
+{
+	return _float_to_base(v, PyLong_Type.tp_as_number->nb_oct);
+}
+
+static PyObject *
+float_bin(PyFloatObject *v)
+{
+	return _float_to_base(v, PyLong_Type.tp_as_number->nb_bin);
+}
 
 static PyObject *
 float_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds);
@@ -1490,8 +1546,8 @@ static PyNumberMethods float_as_number = {
 	float_trunc, 	/*nb_int*/
 	float_trunc, 	/*nb_long*/
 	float_float,	/*nb_float*/
-	0,		/* nb_oct */
-	0,		/* nb_hex */
+	(unaryfunc)float_oct,		/* nb_oct */
+	(unaryfunc)float_hex,		/* nb_hex */
 	0,		/* nb_inplace_add */
 	0,		/* nb_inplace_subtract */
 	0,		/* nb_inplace_multiply */
@@ -1507,6 +1563,8 @@ static PyNumberMethods float_as_number = {
 	float_div,	/* nb_true_divide */
 	0,		/* nb_inplace_floor_divide */
 	0,		/* nb_inplace_true_divide */
+	0,		/* nb_index */
+	(unaryfunc)float_bin,		/* nb_bin */
 };
 
 PyTypeObject PyFloat_Type = {