diff --git a/lib/matplotlib/cbook/__init__.py b/lib/matplotlib/cbook/__init__.py
index 9d0fcadc431c..b068fbb1d84a 100644
--- a/lib/matplotlib/cbook/__init__.py
+++ b/lib/matplotlib/cbook/__init__.py
@@ -2212,6 +2212,10 @@ def _g_sig_digits(value, delta):
     Return the number of significant digits to %g-format *value*, assuming that
     it is known with an error of *delta*.
     """
+    if delta == 0:
+        # delta = 0 may occur when trying to format values over a tiny range;
+        # in that case, replace it by the distance to the closest float.
+        delta = np.spacing(value)
     # 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
diff --git a/lib/matplotlib/tests/test_image.py b/lib/matplotlib/tests/test_image.py
index 2c4a2763e4c6..719b19057875 100644
--- a/lib/matplotlib/tests/test_image.py
+++ b/lib/matplotlib/tests/test_image.py
@@ -341,6 +341,7 @@ def test_cursor_data():
         ([[10001, 10000]], "[10001.000]"),
         ([[.123, .987]], "[0.123]"),
         ([[np.nan, 1, 2]], "[]"),
+        ([[1, 1+1e-15]], "[1.0000000000000000]"),
     ])
 def test_format_cursor_data(data, text):
     from matplotlib.backend_bases import MouseEvent