diff -r d0e2437136f5 Doc/library/json.rst
--- a/Doc/library/json.rst	Sun Jan 19 03:01:23 2014 -0800
+++ b/Doc/library/json.rst	Mon Jan 20 12:20:01 2014 +0800
@@ -226,7 +226,9 @@
    *parse_float*, if specified, will be called with the string of every JSON
    float to be decoded.  By default, this is equivalent to ``float(num_str)``.
    This can be used to use another datatype or parser for JSON floats
-   (e.g. :class:`decimal.Decimal`).
+   (e.g. :class:`decimal.Decimal`).  However, if we give a valid Python float
+   but an invalid JSON float, such as '.5', the float will be rejected because
+   JSON parser only accepts a valid JSON float.
 
    *parse_int*, if specified, will be called with the string of every JSON int
    to be decoded.  By default, this is equivalent to ``int(num_str)``.  This can
@@ -312,7 +314,9 @@
    *parse_float*, if specified, will be called with the string of every JSON
    float to be decoded.  By default, this is equivalent to ``float(num_str)``.
    This can be used to use another datatype or parser for JSON floats
-   (e.g. :class:`decimal.Decimal`).
+   (e.g. :class:`decimal.Decimal`).  However, if we give a valid Python float
+   but an invalid JSON float, such as '.5', the float will be rejected because
+   JSON parser only accepts a valid JSON float.
 
    *parse_int*, if specified, will be called with the string of every JSON int
    to be decoded.  By default, this is equivalent to ``int(num_str)``.  This can
diff -r d0e2437136f5 Lib/test/test_json/test_fail.py
--- a/Lib/test/test_json/test_fail.py	Sun Jan 19 03:01:23 2014 -0800
+++ b/Lib/test/test_json/test_fail.py	Mon Jan 20 12:20:01 2014 +0800
@@ -71,6 +71,8 @@
     '["mismatch"}',
     # http://code.google.com/p/simplejson/issues/detail?id=3
     '["A\u001FZ control characters in string"]',
+    # A valid Python number string but an invalid JSON number string
+    '[.5]',
 ]
 
 SKIPS = {