diff --git a/pkgs/racket-doc/scribblings/reference/numbers.scrbl b/pkgs/racket-doc/scribblings/reference/numbers.scrbl
index 5356960894..fe1348b917 100644
--- a/pkgs/racket-doc/scribblings/reference/numbers.scrbl
+++ b/pkgs/racket-doc/scribblings/reference/numbers.scrbl
@@ -1299,7 +1299,7 @@ Returns @racket[#t] if @racket[x] is @racket[+inf.0], @racket[-inf.0], @racket[+
  @racket[#t] for non-negative @racket[inexact?] integers.}
 
 @defproc[(natural? [x any/c]) boolean?]{
- An alias for @racket[nonnegative-integer?].}
+ An alias for @racket[exact-nonnegative-integer?].}
 
 @; ----------------------------------------------------------------------
 @close-eval[math-eval]
diff --git a/pkgs/racket-test-core/tests/racket/math.rktl b/pkgs/racket-test-core/tests/racket/math.rktl
index b1d610cd1a..f326793384 100644
--- a/pkgs/racket-test-core/tests/racket/math.rktl
+++ b/pkgs/racket-test-core/tests/racket/math.rktl
@@ -178,12 +178,12 @@
 ;; natural?
 
 (test #t natural? 1)
-(test #t natural? 1.0)
 (test #t natural? 3/3)
 (test #t natural? 0)
 (test #t natural? -0)
-(test #t natural? 0.0)
-(test #t natural? -0.0)
+(test #f natural? 1.0)
+(test #f natural? 0.0)
+(test #f natural? -0.0)
 (test #f natural? 3/2)
 (test #f natural? 0.5)
 (test #f natural? -5)
diff --git a/racket/collects/racket/math.rkt b/racket/collects/racket/math.rkt
index c3b3e3a746..f22a9b8ba1 100644
--- a/racket/collects/racket/math.rkt
+++ b/racket/collects/racket/math.rkt
@@ -47,7 +47,7 @@
   (define (nonnegative-integer? x)
     (and (integer? x) (not (negative? x))))
 
-  (define natural? nonnegative-integer?)
+  (define natural? exact-nonnegative-integer?)
 
   ;; z^2
   (define (sqr z)