diff --git a/lib/matplotlib/axis.py b/lib/matplotlib/axis.py
index ac6bf3425c41..fd92bb5c5214 100644
--- a/lib/matplotlib/axis.py
+++ b/lib/matplotlib/axis.py
@@ -1498,6 +1498,10 @@ def have_units(self):
         return self.converter is not None or self.units is not None
 
     def convert_units(self, x):
+        # If x is already a number, doesn't need converting
+        if munits.ConversionInterface.is_numlike(x):
+            return x
+
         if self.converter is None:
             self.converter = munits.registry.get_converter(x)
 
diff --git a/lib/matplotlib/dates.py b/lib/matplotlib/dates.py
index f71f12eea32e..702959e2feab 100644
--- a/lib/matplotlib/dates.py
+++ b/lib/matplotlib/dates.py
@@ -1738,8 +1738,6 @@ def convert(value, unit, axis):
 
         The *unit* and *axis* arguments are not used.
         """
-        if units.ConversionInterface.is_numlike(value):
-            return value
         return date2num(value)
 
     @staticmethod
diff --git a/lib/matplotlib/tests/test_units.py b/lib/matplotlib/tests/test_units.py
index f72ac2c60476..14e8341e4b5d 100644
--- a/lib/matplotlib/tests/test_units.py
+++ b/lib/matplotlib/tests/test_units.py
@@ -31,7 +31,10 @@ def __getattr__(self, attr):
         return getattr(self.magnitude, attr)
 
     def __getitem__(self, item):
-        return Quantity(self.magnitude[item], self.units)
+        if iterable(self.magnitude):
+            return Quantity(self.magnitude[item], self.units)
+        else:
+            return Quantity(self.magnitude, self.units)
 
     def __array__(self):
         return np.asarray(self.magnitude)