diff --git a/Lib/test/test_format.py b/Lib/test/test_format.py
index 4559cd5623e..e9e5bb9cf00 100644
--- a/Lib/test/test_format.py
+++ b/Lib/test/test_format.py
@@ -484,6 +484,17 @@ class FormatTest(unittest.TestCase):
         with self.assertRaises(ValueError) as cm:
             format(c, ".%sf" % (INT_MAX + 1))
 
+    def test_g_format_has_no_trailing_zeros(self):
+        # regression test for bugs.python.org/issue40780
+        self.assertEqual("%.3g" % 1505.0, "1.5e+03")
+        self.assertEqual("%#.3g" % 1505.0, "1.50e+03")
+
+        self.assertEqual(format(1505.0, ".3g"), "1.5e+03")
+        self.assertEqual(format(1505.0, "#.3g"), "1.50e+03")
+
+        self.assertEqual(format(12300050.0, ".6g"), "1.23e+07")
+        self.assertEqual(format(12300050.0, "#.6g"), "1.23000e+07")
+
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/Misc/NEWS.d/next/Core and Builtins/2020-05-26-17-43-58.bpo-40780.3Ckdgm.rst b/Misc/NEWS.d/next/Core and Builtins/2020-05-26-17-43-58.bpo-40780.3Ckdgm.rst
new file mode 100644
index 00000000000..ed6020c2e23
--- /dev/null
+++ b/Misc/NEWS.d/next/Core and Builtins/2020-05-26-17-43-58.bpo-40780.3Ckdgm.rst	
@@ -0,0 +1,2 @@
+Fix a corner case where g-style string formatting of a float failed to
+remove trailing zeros.
diff --git a/Python/dtoa.c b/Python/dtoa.c
index 822adc61296..e629b296426 100644
--- a/Python/dtoa.c
+++ b/Python/dtoa.c
@@ -64,6 +64,9 @@
  *  7. _Py_dg_strtod has been modified so that it doesn't accept strings with
  *     leading whitespace.
  *
+ *  8. A corner case where _Py_dg_dtoa didn't strip trailing zeros has been
+ *     fixed. (bugs.python.org/issue40780)
+ *
  ***************************************************************/
 
 /* Please send bug reports for the original dtoa.c code to David M. Gay (dmg
@@ -2563,6 +2566,14 @@ _Py_dg_dtoa(double dd, int mode, int ndigits,
                         }
                     ++*s++;
                 }
+                else {
+                    /* Strip trailing zeros. This branch was missing from the
+                       original dtoa.c, leading to surplus trailing zeros in
+                       some cases. See bugs.python.org/issue40780. */
+                    while (s > s0 && s[-1] == '0') {
+                        --s;
+                    }
+                }
                 break;
             }
         }