diff --git a/doc/users/next_whats_new/2020-03-15-cursor-sigdigits.rst b/doc/users/next_whats_new/2020-03-15-cursor-sigdigits.rst
@@ -0,0 +1,6 @@
+Cursor text now uses a number of significant digits matching pointing precision
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+Previously, the x/y position displayed by the cursor text would usually include
+far more significant digits than the mouse pointing precision (typically one
+pixel).  This is now fixed for linear scales.
diff --git a/lib/matplotlib/tests/test_ticker.py b/lib/matplotlib/tests/test_ticker.py
@@ -558,6 +558,16 @@ def test_scilimits(self, sci_type, scilimits, lim, orderOfMag, fewticks):
         tmp_form.set_locs(ax.yaxis.get_majorticklocs())
         assert orderOfMag == tmp_form.orderOfMagnitude
 
+    def test_cursor_precision(self):
+        fig, ax = plt.subplots()
+        ax.set_xlim(-1, 1)  # Pointing precision of 0.001.
+        fmt = ax.xaxis.get_major_formatter().format_data_short
+        assert fmt(0.) == "0.000"
+        assert fmt(0.0123) == "0.012"
+        assert fmt(0.123) == "0.123"
+        assert fmt(1.23) == "1.230"
+        assert fmt(12.3) == "12.300"
+
 
 class FakeAxis:
     """Allow Formatter to be called without having a "full" plot set up."""

diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
@@ -168,6 +168,7 @@
 import logging
 import locale
 import math
+from numbers import Integral
 
 import numpy as np
 
@@ -587,11 +588,42 @@ def set_powerlimits(self, lims):
 
     def format_data_short(self, value):
         # docstring inherited
+        if isinstance(value, np.ma.MaskedArray) and value.mask:
+            return ""
+        if isinstance(value, Integral):
+            fmt = "%d"
+        else:
+            if self.axis.__name__ in ["xaxis", "yaxis"]:
+                if self.axis.__name__ == "xaxis":
+                    axis_trf = self.axis.axes.get_xaxis_transform()
+                    axis_inv_trf = axis_trf.inverted()
+                    screen_xy = axis_trf.transform((value, 0))
+                    neighbor_values = axis_inv_trf.transform(
+                        screen_xy + [[-1, 0], [+1, 0]])[:, 0]
+                else:  # yaxis:
+                    axis_trf = self.axis.axes.get_yaxis_transform()
+                    axis_inv_trf = axis_trf.inverted()
+                    screen_xy = axis_trf.transform((0, value))
+                    neighbor_values = axis_inv_trf.transform(
+                        screen_xy + [[0, -1], [0, +1]])[:, 1]
+                delta = abs(neighbor_values - value).max()
+            else:
+                # Rough approximation: no more than 1e4 pixels.
+                delta = self.axis.get_view_interval() / 1e4
+            # If e.g. value = 45.67 and delta = 0.02, then we want to round to
+            # 2 digits after the decimal point (floor(log10(0.02)) = -2);
+            # 45.67 contributes 2 digits before the decimal point
+            # (floor(log10(45.67)) + 1 = 2): the total is 4 significant digits.
+            # A value of 0 contributes 1 "digit" before the decimal point.
+            sig_digits = max(
+                0,
+                (math.floor(math.log10(abs(value))) + 1 if value else 1)
+                - math.floor(math.log10(delta)))
+            fmt = f"%-#.{sig_digits}g"
         return (
-            "" if isinstance(value, np.ma.MaskedArray) and value.mask else
             self.fix_minus(
-                locale.format_string("%-12g", (value,)) if self._useLocale else
-                "%-12g" % value))
+                locale.format_string(fmt, (value,)) if self._useLocale else
+                fmt % value))
 
     def format_data(self, value):
         # docstring inherited