diff --git a/Lib/test/test_grammar.py b/Lib/test/test_grammar.py
index a7bad2d2d9d..b363f9936df 100644
--- a/Lib/test/test_grammar.py
+++ b/Lib/test/test_grammar.py
@@ -80,6 +80,12 @@ def test_floats(self):
         x = .3e14
         x = 3.1e4
 
+    def test_float_exponent_tokenization(self):
+        # See issue 21642.
+        self.assertEqual(1 if 1else 0, 1)
+        self.assertEqual(1 if 0else 0, 0)
+        self.assertRaises(SyntaxError, eval, "0 if 1Else 0")
+
     def test_string_literals(self):
         x = ''; y = ""; self.assertTrue(len(x) == 0 and x == y)
         x = '\''; y = "'"; self.assertTrue(len(x) == 1 and x == y and ord(x) == 39)
diff --git a/Misc/NEWS b/Misc/NEWS
index caf6c1819f5..62c1be00ba5 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -10,6 +10,10 @@ Release date: TBA
 Core and Builtins
 -----------------
 
+- Issue #21642: If the conditional if-else expression, allow an integer written
+  with no space between itself and the ``else`` keyword (e.g. ``True if 42else
+  False``) to be valid syntax.
+
 - Issue #21523: Fix over-pessimistic computation of the stack effect of
   some opcodes in the compiler.  This also fixes a quadratic compilation
   time issue noticeable when compiling code with a large number of "and"
diff --git a/Parser/tokenizer.c b/Parser/tokenizer.c
index 6aaa4a9d383..ef7b19fb42f 100644
--- a/Parser/tokenizer.c
+++ b/Parser/tokenizer.c
@@ -1603,15 +1603,24 @@ tok_get(struct tok_state *tok, char **p_start, char **p_end)
                     } while (isdigit(c));
                 }
                 if (c == 'e' || c == 'E') {
-        exponent:
+                    int e;
+                  exponent:
+                    e = c;
                     /* Exponent part */
                     c = tok_nextc(tok);
-                    if (c == '+' || c == '-')
+                    if (c == '+' || c == '-') {
                         c = tok_nextc(tok);
-                    if (!isdigit(c)) {
-                        tok->done = E_TOKEN;
+                        if (!isdigit(c)) {
+                            tok->done = E_TOKEN;
+                            tok_backup(tok, c);
+                            return ERRORTOKEN;
+                        }
+                    } else if (!isdigit(c)) {
                         tok_backup(tok, c);
-                        return ERRORTOKEN;
+                        tok_backup(tok, e);
+                        *p_start = tok->start;
+                        *p_end = tok->cur;
+                        return NUMBER;
                     }
                     do {
                         c = tok_nextc(tok);