diff --git a/doc/source/whatsnew/v0.16.1.txt b/doc/source/whatsnew/v0.16.1.txt
index 8c49e2780ed06..6fc347cfeb273 100644
--- a/doc/source/whatsnew/v0.16.1.txt
+++ b/doc/source/whatsnew/v0.16.1.txt
@@ -79,3 +79,4 @@ Bug Fixes
 
 - Bug in ``Series.quantile`` on empty Series of type ``Datetime`` or ``Timedelta`` (:issue:`9675`)
 - Bug in ``where`` causing incorrect results when upcasting was required (:issue:`9731`)
+- Bug in ``FloatArrayFormatter`` where decision boundary for displaying "small" floats in decimal format is off by one order of magnitude for a given display.precision (:issue:`9764`)
diff --git a/pandas/core/format.py b/pandas/core/format.py
index b21ca9050ffd0..7b8a3161b5e05 100644
--- a/pandas/core/format.py
+++ b/pandas/core/format.py
@@ -1996,7 +1996,7 @@ def _format_strings(self):
 
             # this is pretty arbitrary for now
             has_large_values = (abs_vals > 1e8).any()
-            has_small_values = ((abs_vals < 10 ** (-self.digits)) &
+            has_small_values = ((abs_vals < 10 ** (-self.digits+1)) &
                                 (abs_vals > 0)).any()
 
             if too_long and has_large_values:
diff --git a/pandas/tests/test_format.py b/pandas/tests/test_format.py
index ce32c8af99a73..1dcdbf12a6b59 100644
--- a/pandas/tests/test_format.py
+++ b/pandas/tests/test_format.py
@@ -2986,6 +2986,25 @@ def test_format(self):
         self.assertEqual(result[0], " 12")
         self.assertEqual(result[1], "  0")
 
+    def test_output_significant_digits(self):
+        # Issue #9764
+        
+        # In case default display precision changes:
+        with pd.option_context('display.precision', 7):
+            # DataFrame example from issue #9764
+            d=pd.DataFrame({'col1':[9.999e-8, 1e-7, 1.0001e-7, 2e-7, 4.999e-7, 5e-7, 5.0001e-7, 6e-7, 9.999e-7, 1e-6, 1.0001e-6, 2e-6, 4.999e-6, 5e-6, 5.0001e-6, 6e-6]})
+            
+            expected_output={
+                (0,6):'           col1\n0  9.999000e-08\n1  1.000000e-07\n2  1.000100e-07\n3  2.000000e-07\n4  4.999000e-07\n5  5.000000e-07',
+                (1,6):'           col1\n1  1.000000e-07\n2  1.000100e-07\n3  2.000000e-07\n4  4.999000e-07\n5  5.000000e-07',
+                (1,8):'           col1\n1  1.000000e-07\n2  1.000100e-07\n3  2.000000e-07\n4  4.999000e-07\n5  5.000000e-07\n6  5.000100e-07\n7  6.000000e-07',
+                (8,16):'            col1\n8   9.999000e-07\n9   1.000000e-06\n10  1.000100e-06\n11  2.000000e-06\n12  4.999000e-06\n13  5.000000e-06\n14  5.000100e-06\n15  6.000000e-06',
+                (9,16):'        col1\n9   0.000001\n10  0.000001\n11  0.000002\n12  0.000005\n13  0.000005\n14  0.000005\n15  0.000006'
+            }
+
+            for (start, stop), v in expected_output.items():
+                self.assertEqual(str(d[start:stop]), v)
+
 
 class TestRepr_timedelta64(tm.TestCase):