diff --git a/rest_framework/pagination.py b/rest_framework/pagination.py
index 2c3b0d2a5..dfdadc329 100644
--- a/rest_framework/pagination.py
+++ b/rest_framework/pagination.py
@@ -7,6 +7,7 @@ from __future__ import unicode_literals
 
 from base64 import b64decode, b64encode
 from collections import OrderedDict, namedtuple
+import decimal
 
 from django.core.paginator import Paginator as DjangoPaginator
 from django.core.paginator import InvalidPage
@@ -497,6 +498,9 @@ class CursorPagination(BasePagination):
     # queries, by having a hard cap on the maximum possible size of the offset.
     offset_cutoff = 1000
 
+    __rounding_down = decimal.Context(prec=14, rounding=decimal.ROUND_FLOOR)
+    __rounding_up = decimal.Context(prec=14, rounding=decimal.ROUND_CEILING)
+
     def paginate_queryset(self, queryset, request, view=None):
         self.page_size = self.get_page_size(request)
         if not self.page_size:
@@ -775,6 +779,13 @@ class CursorPagination(BasePagination):
             attr = instance[field_name]
         else:
             attr = getattr(instance, field_name)
+
+        if isinstance(attr, float):
+            if ordering[0][0] == '-':
+                attr = self.__rounding_down.create_decimal_from_float(attr)
+            else:
+                attr = self.__rounding_up.create_decimal_from_float(attr)
+
         return six.text_type(attr)
 
     def get_paginated_response(self, data):
diff --git a/tests/test_pagination.py b/tests/test_pagination.py
index d9ad9e6f6..e50eb440c 100644
--- a/tests/test_pagination.py
+++ b/tests/test_pagination.py
@@ -7,9 +7,9 @@ from django.db import models
 from django.test import TestCase
 
 from rest_framework import (
-    exceptions, filters, generics, pagination, serializers, status
+    exceptions, filters, generics, pagination, serializers, status, viewsets
 )
-from rest_framework.pagination import PAGE_BREAK, PageLink
+from rest_framework.pagination import CursorPagination, PAGE_BREAK, PageLink
 from rest_framework.request import Request
 from rest_framework.test import APIRequestFactory
 
@@ -986,3 +986,46 @@ def test_get_displayed_page_numbers():
     assert displayed_page_numbers(7, 9) == [1, None, 6, 7, 8, 9]
     assert displayed_page_numbers(8, 9) == [1, None, 7, 8, 9]
     assert displayed_page_numbers(9, 9) == [1, None, 7, 8, 9]
+
+
+class ThreeItemCursorPagination(CursorPagination):
+    page_size = 3
+    ordering = 'score'
+
+
+class FloatyModel(models.Model):
+    score = models.FloatField()
+
+
+class PassThroughSerializer(serializers.BaseSerializer):
+    def to_representation(self, item):
+        return item
+
+
+class FloatyViewSet(viewsets.ReadOnlyModelViewSet):
+    queryset = FloatyModel.objects.all()
+    pagination_class = ThreeItemCursorPagination
+    serializer_class = PassThroughSerializer
+    page_size = 3
+
+
+class TestCursorPaginationWithFloatingPointPosition(TestCase):
+    def setUp(self):
+        self.view = FloatyViewSet.as_view(actions={'get': 'list'})
+
+    def test_page_boundary_does_not_repeat_elements(self):
+        for i in range(12):
+            FloatyModel.objects.create(score=i/9.0)
+
+        request = factory.get('/')
+        first_response = self.view(request)
+
+        first_page_last_item = first_response.data['results'][-1]
+
+        second_request = factory.get(first_response.data['next'])
+        second_response = self.view(second_request)
+
+        second_page_first_item = second_response.data['results'][0]
+
+        self.assertNotEqual(first_page_last_item.pk, second_page_first_item.pk)
+        self.assertLess(first_page_last_item.score, second_page_first_item.score)