diff --git a/django/db/migrations/writer.py b/django/db/migrations/writer.py
index f6f01d943f..53ec414335 100644
--- a/django/db/migrations/writer.py
+++ b/django/db/migrations/writer.py
@@ -1,10 +1,11 @@
 from __future__ import unicode_literals
 
-import datetime
-import inspect
-import decimal
 import collections
+import datetime
+import decimal
 from importlib import import_module
+import inspect
+import math
 import os
 import re
 import sys
@@ -303,7 +304,11 @@ class MigrationWriter(object):
         elif isinstance(value, SettingsReference):
             return "settings.%s" % value.setting_name, set(["from django.conf import settings"])
         # Simple types
-        elif isinstance(value, six.integer_types + (float, bool, type(None))):
+        elif isinstance(value, float):
+            if math.isnan(value) or math.isinf(value):
+                return 'float("{}")'.format(value), set()
+            return repr(value), set()
+        elif isinstance(value, six.integer_types + (bool, type(None))):
             return repr(value), set()
         elif isinstance(value, six.binary_type):
             value_repr = repr(value)
diff --git a/docs/releases/1.7.2.txt b/docs/releases/1.7.2.txt
index eaaf15507a..3d9a74616b 100644
--- a/docs/releases/1.7.2.txt
+++ b/docs/releases/1.7.2.txt
@@ -49,3 +49,6 @@ Bugfixes
 
 * Allowed usage of ``DateTimeField()`` as ``Transform.output_field``
   (:ticket:`23420`).
+
+* Fixed a migration serializing bug involving ``float("nan")`` and
+  ``float("inf")`` (:ticket:23770:).
diff --git a/tests/migrations/test_writer.py b/tests/migrations/test_writer.py
index 0503270ed2..cb9ed5d0d5 100644
--- a/tests/migrations/test_writer.py
+++ b/tests/migrations/test_writer.py
@@ -2,6 +2,7 @@
 from __future__ import unicode_literals
 
 import datetime
+import math
 import os
 import re
 import tokenize
@@ -69,6 +70,10 @@ class WriterTests(TestCase):
         """
         # Basic values
         self.assertSerializedEqual(1)
+        self.assertSerializedEqual(1.2)
+        self.assertTrue(math.isinf(self.serialize_round_trip(float("inf"))))
+        self.assertTrue(math.isinf(self.serialize_round_trip(float("-inf"))))
+        self.assertTrue(math.isnan(self.serialize_round_trip(float("nan"))))
         self.assertSerializedEqual(None)
         self.assertSerializedEqual(b"foobar")
         string, imports = MigrationWriter.serialize(b"foobar")