diff --git a/doc/lispref/numbers.texi b/doc/lispref/numbers.texi
index 4c5f72126ed..d28e15869aa 100644
--- a/doc/lispref/numbers.texi
+++ b/doc/lispref/numbers.texi
@@ -237,7 +237,8 @@ precede the number and its exponent.  For example, @samp{1500.0},
 @samp{+15e2}, @samp{15.0e+2}, @samp{+1500000e-3}, and @samp{.15e4} are
 five ways of writing a floating-point number whose value is 1500.
 They are all equivalent.  Like Common Lisp, Emacs Lisp requires at
-least one digit after any decimal point in a floating-point number;
+least one digit after a decimal point in a floating-point number that
+does not have an exponent;
 @samp{1500.} is an integer, not a floating-point number.
 
   Emacs Lisp treats @code{-0.0} as numerically equal to ordinary zero
diff --git a/src/lread.c b/src/lread.c
index bca53a9a37a..0b33fd0f254 100644
--- a/src/lread.c
+++ b/src/lread.c
@@ -3938,8 +3938,7 @@ string_to_number (char const *string, int base, ptrdiff_t *plen)
   bool signedp = negative | positive;
   cp += signedp;
 
-  enum { INTOVERFLOW = 1, LEAD_INT = 2, DOT_CHAR = 4, TRAIL_INT = 8,
-	 E_EXP = 16 };
+  enum { INTOVERFLOW = 1, LEAD_INT = 2, TRAIL_INT = 4, E_EXP = 16 };
   int state = 0;
   int leading_digit = digit_to_number (*cp, base);
   uintmax_t n = leading_digit;
@@ -3959,7 +3958,6 @@ string_to_number (char const *string, int base, ptrdiff_t *plen)
   char const *after_digits = cp;
   if (*cp == '.')
     {
-      state |= DOT_CHAR;
       cp++;
     }
 
@@ -4008,8 +4006,10 @@ string_to_number (char const *string, int base, ptrdiff_t *plen)
 	    cp = ecp;
 	}
 
-      float_syntax = ((state & (DOT_CHAR|TRAIL_INT)) == (DOT_CHAR|TRAIL_INT)
-		      || (state & ~INTOVERFLOW) == (LEAD_INT|E_EXP));
+      /* A float has digits after the dot or an exponent.
+	 This excludes numbers like "1." which are lexed as integers. */
+      float_syntax = ((state & TRAIL_INT)
+		      || ((state & LEAD_INT) && (state & E_EXP)));
     }
 
   if (plen)
diff --git a/test/src/lread-tests.el b/test/src/lread-tests.el
index f2a60bcf327..dac8f95bc4d 100644
--- a/test/src/lread-tests.el
+++ b/test/src/lread-tests.el
@@ -196,4 +196,71 @@ literals (Bug#20852)."
     (should-error (read-event "foo: "))
     (should-error (read-char-exclusive "foo: "))))
 
+(ert-deftest lread-float ()
+  (should (equal (read "13") 13))
+  (should (equal (read "+13") 13))
+  (should (equal (read "-13") -13))
+  (should (equal (read "13.") 13))
+  (should (equal (read "+13.") 13))
+  (should (equal (read "-13.") -13))
+  (should (equal (read "13.25") 13.25))
+  (should (equal (read "+13.25") 13.25))
+  (should (equal (read "-13.25") -13.25))
+  (should (equal (read ".25") 0.25))
+  (should (equal (read "+.25") 0.25))
+  (should (equal (read "-.25") -0.25))
+  (should (equal (read "13e4") 130000.0))
+  (should (equal (read "+13e4") 130000.0))
+  (should (equal (read "-13e4") -130000.0))
+  (should (equal (read "13e+4") 130000.0))
+  (should (equal (read "+13e+4") 130000.0))
+  (should (equal (read "-13e+4") -130000.0))
+  (should (equal (read "625e-4") 0.0625))
+  (should (equal (read "+625e-4") 0.0625))
+  (should (equal (read "-625e-4") -0.0625))
+  (should (equal (read "1.25e2") 125.0))
+  (should (equal (read "+1.25e2") 125.0))
+  (should (equal (read "-1.25e2") -125.0))
+  (should (equal (read "1.25e+2") 125.0))
+  (should (equal (read "+1.25e+2") 125.0))
+  (should (equal (read "-1.25e+2") -125.0))
+  (should (equal (read "1.25e-1") 0.125))
+  (should (equal (read "+1.25e-1") 0.125))
+  (should (equal (read "-1.25e-1") -0.125))
+  (should (equal (read "4.e3") 4000.0))
+  (should (equal (read "+4.e3") 4000.0))
+  (should (equal (read "-4.e3") -4000.0))
+  (should (equal (read "4.e+3") 4000.0))
+  (should (equal (read "+4.e+3") 4000.0))
+  (should (equal (read "-4.e+3") -4000.0))
+  (should (equal (read "5.e-1") 0.5))
+  (should (equal (read "+5.e-1") 0.5))
+  (should (equal (read "-5.e-1") -0.5))
+  (should (equal (read "0") 0))
+  (should (equal (read "+0") 0))
+  (should (equal (read "-0") 0))
+  (should (equal (read "0.") 0))
+  (should (equal (read "+0.") 0))
+  (should (equal (read "-0.") 0))
+  (should (equal (read "0.0") 0.0))
+  (should (equal (read "+0.0") 0.0))
+  (should (equal (read "-0.0") -0.0))
+  (should (equal (read "0e5") 0.0))
+  (should (equal (read "+0e5") 0.0))
+  (should (equal (read "-0e5") -0.0))
+  (should (equal (read "0e-5") 0.0))
+  (should (equal (read "+0e-5") 0.0))
+  (should (equal (read "-0e-5") -0.0))
+  (should (equal (read ".0e-5") 0.0))
+  (should (equal (read "+.0e-5") 0.0))
+  (should (equal (read "-.0e-5") -0.0))
+  (should (equal (read "0.0e-5") 0.0))
+  (should (equal (read "+0.0e-5") 0.0))
+  (should (equal (read "-0.0e-5") -0.0))
+  (should (equal (read "0.e-5") 0.0))
+  (should (equal (read "+0.e-5") 0.0))
+  (should (equal (read "-0.e-5") -0.0))
+  )
+
+
 ;;; lread-tests.el ends here