diff --git a/prometheus_client/openmetrics/parser.py b/prometheus_client/openmetrics/parser.py
index a167ae6e..6235eda5 100644
--- a/prometheus_client/openmetrics/parser.py
+++ b/prometheus_client/openmetrics/parser.py
@@ -15,7 +15,6 @@
     # Python 3
     import io as StringIO
 
-
 def text_string_to_metric_families(text):
     """Parse Openmetrics text format from a unicode string.
 
@@ -25,6 +24,16 @@ def text_string_to_metric_families(text):
         yield metric_family
 
 
+_CANONICAL_NUMBERS = set([i / 1000.0 for i in range(10000)] + [10.0**i for i in range(-10, 11)] + [float("inf")])
+
+
+def _isUncanonicalNumber(s):
+    f = float(s)
+    if f not in _CANONICAL_NUMBERS:
+        return False  # Only the canonical numbers are required to be canonical.
+    return s != floatToGoString(f)
+
+
 ESCAPE_SEQUENCES = {
     '\\\\': '\\',
     '\\n': '\n',
@@ -544,11 +553,11 @@ def build_metric(name, documentation, typ, unit, samples):
                 raise ValueError("Stateset missing label: " + line)
             if (typ in ['histogram', 'gaugehistogram'] and name + '_bucket' == sample.name
                     and (sample.labels.get('le', "NaN") == "NaN"
-                         or sample.labels['le'] != floatToGoString(sample.labels['le']))):
+                         or _isUncanonicalNumber(sample.labels['le']))):
                 raise ValueError("Invalid le label: " + line)
             if (typ == 'summary' and name == sample.name
                     and (not (0 <= float(sample.labels.get('quantile', -1)) <= 1)
-                         or sample.labels['quantile'] != floatToGoString(sample.labels['quantile']))):
+                          or _isUncanonicalNumber(sample.labels['quantile']))):
                 raise ValueError("Invalid quantile label: " + line)
 
             g = tuple(sorted(_group_for_sample(sample, name, typ).items()))
diff --git a/tests/openmetrics/test_parser.py b/tests/openmetrics/test_parser.py
index abdf1816..81525d34 100644
--- a/tests/openmetrics/test_parser.py
+++ b/tests/openmetrics/test_parser.py
@@ -122,6 +122,20 @@ def test_simple_histogram(self):
         self.assertEqual([HistogramMetricFamily("a", "help", sum_value=2, buckets=[("1.0", 0.0), ("+Inf", 3.0)])],
                          list(families))
 
+    def test_histogram_noncanonical(self):
+        families = text_string_to_metric_families("""# TYPE a histogram
+# HELP a help
+a_bucket{le="0.00000000001"} 0
+a_bucket{le="1.1e-4"} 0
+a_bucket{le="1.1e-3"} 0
+a_bucket{le="100000000000.0"} 0
+a_bucket{le="+Inf"} 3
+a_count 3
+a_sum 2
+# EOF
+""")
+        list(families)
+
     def test_negative_bucket_histogram(self):
         families = text_string_to_metric_families("""# TYPE a histogram
 # HELP a help
@@ -731,9 +745,13 @@ def test_invalid_input(self):
             ('# TYPE a gaugehistogram\na_gsum 1\n# EOF\n'),
             ('# TYPE a histogram\na_count 1\na_bucket{le="+Inf"} 0\n# EOF\n'),
             ('# TYPE a histogram\na_bucket{le="+Inf"} 0\na_count 1\n# EOF\n'),
+            ('# TYPE a histogram\na_bucket{le="0"} 0\na_bucket{le="+Inf"} 0\n# EOF\n'),
             ('# TYPE a histogram\na_bucket{le="1"} 0\na_bucket{le="+Inf"} 0\n# EOF\n'),
+            ('# TYPE a histogram\na_bucket{le="0.0000000001"} 0\na_bucket{le="+Inf"} 0\n# EOF\n'),
+            ('# TYPE a histogram\na_bucket{le="1.1e-2"} 0\na_bucket{le="+Inf"} 0\n# EOF\n'),
             ('# TYPE a histogram\na_bucket{le="1e-04"} 0\na_bucket{le="+Inf"} 0\n# EOF\n'),
             ('# TYPE a histogram\na_bucket{le="1e+05"} 0\na_bucket{le="+Inf"} 0\n# EOF\n'),
+            ('# TYPE a histogram\na_bucket{le="10000000000"} 0\na_bucket{le="+Inf"} 0\n# EOF\n'),
             ('# TYPE a histogram\na_bucket{le="+INF"} 0\n# EOF\n'),
             ('# TYPE a histogram\na_bucket{le="2"} 0\na_bucket{le="1"} 0\na_bucket{le="+Inf"} 0\n# EOF\n'),
             ('# TYPE a histogram\na_bucket{le="1"} 1\na_bucket{le="2"} 1\na_bucket{le="+Inf"} 0\n# EOF\n'),
@@ -754,16 +772,6 @@ def test_invalid_input(self):
             with self.assertRaises(ValueError, msg=case):
                 list(text_string_to_metric_families(case))
 
-    @unittest.skipIf(sys.version_info < (2, 7), "float repr changed from 2.6 to 2.7")
-    def test_invalid_float_input(self):
-        for case in [
-            # Bad histograms.
-            ('# TYPE a histogram\na_bucket{le="9.999999999999999e+22"} 0\na_bucket{le="+Inf"} 0\n# EOF\n'),
-            ('# TYPE a histogram\na_bucket{le="1.5555555555555201e+06"} 0\na_bucket{le="+Inf"} 0\n# EOF\n'),
-        ]:
-            with self.assertRaises(ValueError):
-                list(text_string_to_metric_families(case))
-
 
 if __name__ == '__main__':
     unittest.main()