diff --git a/docker/api/container.py b/docker/api/container.py
index cf5caebbf6..24eb9c1ca5 100644
--- a/docker/api/container.py
+++ b/docker/api/container.py
@@ -506,7 +506,7 @@ def create_host_config(self, *args, **kwargs):
                 bytes) or a string with a units identification char
                 (``100000b``, ``1000k``, ``128m``, ``1g``). If a string is
                 specified without a units character, bytes are assumed as an
-            mem_reservation (int or str): Memory soft limit.
+            mem_reservation (float or str): Memory soft limit.
             mem_swappiness (int): Tune a container's memory swappiness
                 behavior. Accepts number between 0 and 100.
             memswap_limit (str or int): Maximum amount of memory + swap a
@@ -1219,8 +1219,8 @@ def update_container(
             cpu_shares (int): CPU shares (relative weight)
             cpuset_cpus (str): CPUs in which to allow execution
             cpuset_mems (str): MEMs in which to allow execution
-            mem_limit (int or str): Memory limit
-            mem_reservation (int or str): Memory soft limit
+            mem_limit (float or str): Memory limit
+            mem_reservation (float or str): Memory soft limit
             memswap_limit (int or str): Total memory (memory + swap), -1 to
                 disable swap
             kernel_memory (int or str): Kernel memory limit
diff --git a/docker/utils/utils.py b/docker/utils/utils.py
index 447760b483..1b195e2787 100644
--- a/docker/utils/utils.py
+++ b/docker/utils/utils.py
@@ -412,7 +412,7 @@ def parse_bytes(s):
 
     if suffix in units.keys() or suffix.isdigit():
         try:
-            digits = int(digits_part)
+            digits = float(digits_part)
         except ValueError:
             raise errors.DockerException(
                 'Failed converting the string value for memory ({0}) to'
diff --git a/tests/unit/utils_test.py b/tests/unit/utils_test.py
index d9cb002809..07209a1b13 100644
--- a/tests/unit/utils_test.py
+++ b/tests/unit/utils_test.py
@@ -5,27 +5,21 @@
 import os
 import os.path
 import shutil
-import sys
 import tempfile
 import unittest
 
-
+import pytest
+import six
 from docker.api.client import APIClient
 from docker.constants import IS_WINDOWS_PLATFORM
 from docker.errors import DockerException
-from docker.utils import (
-    convert_filters, convert_volume_binds, decode_json_header, kwargs_from_env,
-    parse_bytes, parse_devices, parse_env_file, parse_host,
-    parse_repository_tag, split_command, update_headers,
-)
-
+from docker.utils import (convert_filters, convert_volume_binds,
+                          decode_json_header, kwargs_from_env, parse_bytes,
+                          parse_devices, parse_env_file, parse_host,
+                          parse_repository_tag, split_command, update_headers)
 from docker.utils.ports import build_port_bindings, split_port
 from docker.utils.utils import format_environment
 
-import pytest
-
-import six
-
 TEST_CERT_DIR = os.path.join(
     os.path.dirname(__file__),
     'testdata/certs',
@@ -447,11 +441,7 @@ def test_parse_bytes_invalid(self):
             parse_bytes("127.0.0.1K")
 
     def test_parse_bytes_float(self):
-        with pytest.raises(DockerException):
-            parse_bytes("1.5k")
-
-    def test_parse_bytes_maxint(self):
-        assert parse_bytes("{0}k".format(sys.maxsize)) == sys.maxsize * 1024
+        assert parse_bytes("1.5k") == 1536
 
 
 class UtilsTest(unittest.TestCase):