diff --git a/lib/matplotlib/tests/test_ticker.py b/lib/matplotlib/tests/test_ticker.py
index c706eaa1599b..baf7373191c5 100644
--- a/lib/matplotlib/tests/test_ticker.py
+++ b/lib/matplotlib/tests/test_ticker.py
@@ -164,48 +164,43 @@ def test_ScalarFormatter_offset_value():
     fig, ax = plt.subplots()
     formatter = ax.get_xaxis().get_major_formatter()
 
-    def update_ticks(ax):
-        return next(ax.get_xaxis().iter_ticks())
-
-    ax.set_xlim(123, 189)
-    update_ticks(ax)
-    assert_equal(formatter.offset, 0)
-
-    ax.set_xlim(-189, -123)
-    update_ticks(ax)
-    assert_equal(formatter.offset, 0)
-
-    ax.set_xlim(12341, 12349)
-    update_ticks(ax)
-    assert_equal(formatter.offset, 12340)
-
-    ax.set_xlim(-12349, -12341)
-    update_ticks(ax)
-    assert_equal(formatter.offset, -12340)
-
-    ax.set_xlim(99999.5, 100010.5)
-    update_ticks(ax)
-    assert_equal(formatter.offset, 100000)
-
-    ax.set_xlim(-100010.5, -99999.5)
-    update_ticks(ax)
-    assert_equal(formatter.offset, -100000)
-
-    ax.set_xlim(99990.5, 100000.5)
-    update_ticks(ax)
-    assert_equal(formatter.offset, 100000)
-
-    ax.set_xlim(-100000.5, -99990.5)
-    update_ticks(ax)
-    assert_equal(formatter.offset, -100000)
-
-    ax.set_xlim(1233999, 1234001)
-    update_ticks(ax)
-    assert_equal(formatter.offset, 1234000)
-
-    ax.set_xlim(-1234001, -1233999)
-    update_ticks(ax)
-    assert_equal(formatter.offset, -1234000)
+    def check_offset_for(left, right, offset):
+        ax.set_xlim(left, right)
+        # Update ticks.
+        next(ax.get_xaxis().iter_ticks())
+        assert_equal(formatter.offset, offset)
+
+    test_data = [(123, 189, 0),
+                 (-189, -123, 0),
+                 (12341, 12349, 12340),
+                 (-12349, -12341, -12340),
+                 (99999.5, 100010.5, 100000),
+                 (-100010.5, -99999.5, -100000),
+                 (99990.5, 100000.5, 100000),
+                 (-100000.5, -99990.5, -100000),
+                 (1233999, 1234001, 1234000),
+                 (-1234001, -1233999, -1234000),
+                 # Test cases courtesy of @WeatherGod
+                 (.4538, .4578, .45),
+                 (3789.12, 3783.1, 3780),
+                 (45124.3, 45831.75, 45000),
+                 (0.000721, 0.0007243, 0.00072),
+                 (12592.82, 12591.43, 12590),
+                 (9., 12., 0),
+                 (900., 1200., 0),
+                 (1900., 1200., 0),
+                 (0.99, 1.01, 1),
+                 (9.99, 10.01, 10),
+                 (99.99, 100.01, 100),
+                 (5.99, 6.01, 6),
+                 (15.99, 16.01, 16),
+                 (-0.452, 0.492, 0),
+                 (-0.492, 0.492, 0),
+                 (12331.4, 12350.5, 12300),
+                 (-12335.3, 12335.3, 0)]
+
+    for left, right, offset in test_data:
+        yield check_offset_for, left, right, offset
 
 
 def _logfe_helper(formatter, base, locs, i, expected_result):
diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
index ecba335d5483..12781fa520a2 100644
--- a/lib/matplotlib/ticker.py
+++ b/lib/matplotlib/ticker.py
@@ -567,34 +567,38 @@ def _compute_offset(self):
         lmin, lmax = locs.min(), locs.max()
         # min, max comparing absolute values (we want division to round towards
         # zero so we work on absolute values).
-        abs_min, abs_max = sorted(map(abs, [lmin, lmax]))
-        # Only use offset if there are at least two ticks, every tick has the
-        # same sign, and if the span is small compared to the absolute values.
-        if (lmin == lmax or lmin <= 0 <= lmax or
-                (abs_max - abs_min) / abs_max >= 1e-2):
+        abs_min, abs_max = sorted([abs(float(lmin)), abs(float(lmax))])
+        # Only use offset if there are at least two ticks and every tick has
+        # the same sign.
+        if lmin == lmax or lmin <= 0 <= lmax:
             self.offset = 0
             return
         sign = math.copysign(1, lmin)
         # What is the smallest power of ten such that abs_min and abs_max are
         # equal up to that precision?
-        oom = 10 ** int(math.log10(abs_max) + 1)
+        # Note: Internally using oom instead of 10 ** oom avoids some numerical
+        # accuracy issues.
+        oom = math.ceil(math.log10(abs_max))
         while True:
-            if abs_min // oom != abs_max // oom:
-                oom *= 10
+            if abs_min // 10 ** oom != abs_max // 10 ** oom:
+                oom += 1
                 break
-            oom /= 10
-        if (abs_max - abs_min) / oom <= 1e-2:
+            oom -= 1
+        if (abs_max - abs_min) / 10 ** oom <= 1e-2:
             # Handle the case of straddling a multiple of a large power of ten
             # (relative to the span).
             # What is the smallest power of ten such that abs_min and abs_max
             # at most 1 apart?
-            oom = 10 ** int(math.log10(abs_max) + 1)
+            oom = math.ceil(math.log10(abs_max))
             while True:
-                if abs_max // oom - abs_min // oom > 1:
-                    oom *= 10
+                if abs_max // 10 ** oom - abs_min // 10 ** oom > 1:
+                    oom += 1
                     break
-                oom /= 10
-        self.offset = sign * (abs_max // oom) * oom
+                oom -= 1
+        # Only use offset if it saves at least two significant digits.
+        self.offset = (sign * (abs_max // 10 ** oom) * 10 ** oom
+                       if abs_max // 10 ** oom >= 10
+                       else 0)
 
     def _set_orderOfMagnitude(self, range):
         # if scientific notation is to be used, find the appropriate exponent