diff --git a/lib/matplotlib/tests/test_ticker.py b/lib/matplotlib/tests/test_ticker.py
index 97328712c224..9d3501059799 100644
--- a/lib/matplotlib/tests/test_ticker.py
+++ b/lib/matplotlib/tests/test_ticker.py
@@ -275,15 +275,17 @@ class TestScalarFormatter(object):
 
     use_offset_data = [True, False]
 
+    #  (sci_type, scilimits, lim, orderOfMag, fewticks)
     scilimits_data = [
-        (False, (0, 0), (10.0, 20.0), 0),
-        (True, (-2, 2), (-10, 20), 0),
-        (True, (-2, 2), (-20, 10), 0),
-        (True, (-2, 2), (-110, 120), 2),
-        (True, (-2, 2), (-120, 110), 2),
-        (True, (-2, 2), (-.001, 0.002), -3),
-        (True, (0, 0), (-1e5, 1e5), 5),
-        (True, (6, 6), (-1e5, 1e5), 6),
+        (False, (0, 0), (10.0, 20.0), 0, False),
+        (True, (-2, 2), (-10, 20), 0, False),
+        (True, (-2, 2), (-20, 10), 0, False),
+        (True, (-2, 2), (-110, 120), 2, False),
+        (True, (-2, 2), (-120, 110), 2, False),
+        (True, (-2, 2), (-.001, 0.002), -3, False),
+        (True, (-7, 7), (0.18e10, 0.83e10), 9, True),
+        (True, (0, 0), (-1e5, 1e5), 5, False),
+        (True, (6, 6), (-1e5, 1e5), 6, False),
     ]
 
     @pytest.mark.parametrize('left, right, offset', offset_data)
@@ -316,14 +318,18 @@ def test_use_offset(self, use_offset):
             assert use_offset == tmp_form.get_useOffset()
 
     @pytest.mark.parametrize(
-        'sci_type, scilimits, lim, orderOfMag', scilimits_data)
-    def test_scilimits(self, sci_type, scilimits, lim, orderOfMag):
+        'sci_type, scilimits, lim, orderOfMag, fewticks', scilimits_data)
+    def test_scilimits(self, sci_type, scilimits, lim, orderOfMag,
+                       fewticks):
         tmp_form = mticker.ScalarFormatter()
         tmp_form.set_scientific(sci_type)
         tmp_form.set_powerlimits(scilimits)
         fig, ax = plt.subplots()
         ax.yaxis.set_major_formatter(tmp_form)
         ax.set_ylim(*lim)
+        if fewticks:
+            ax.yaxis.set_major_locator(mticker.MaxNLocator(4))
+
         tmp_form.set_locs(ax.yaxis.get_majorticklocs())
         assert orderOfMag == tmp_form.orderOfMagnitude
 
diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
index 20c015e7c034..a7487144885e 100644
--- a/lib/matplotlib/ticker.py
+++ b/lib/matplotlib/ticker.py
@@ -712,7 +712,14 @@ def _set_orderOfMagnitude(self, range):
             # fixed scaling when lower power limit = upper <> 0.
             self.orderOfMagnitude = self._powerlimits[0]
             return
-        locs = np.abs(self.locs)
+        # restrict to visible ticks
+        vmin, vmax = sorted(self.axis.get_view_interval())
+        locs = np.asarray(self.locs)
+        locs = locs[(vmin <= locs) & (locs <= vmax)]
+        locs = np.abs(locs)
+        if not len(locs):
+            self.orderOfMagnitude = 0
+            return
         if self.offset:
             oom = math.floor(math.log10(range))
         else: