diff --git a/pkgs/racket-doc/scribblings/reference/numbers.scrbl b/pkgs/racket-doc/scribblings/reference/numbers.scrbl
index 8496654fb3..1d4ed6745f 100644
--- a/pkgs/racket-doc/scribblings/reference/numbers.scrbl
+++ b/pkgs/racket-doc/scribblings/reference/numbers.scrbl
@@ -1116,16 +1116,17 @@ Converts @racket[x] radians to degrees.
 
 Returns @racket[(* z z)].}
 
-@defproc[(sgn [x real?]) (or/c 1 0 -1 1.0 0.0 -1.0)]{
+@defproc[(sgn [x real?]) (or/c (=/c -1) (=/c 0) (=/c 1) +nan.0 +nan.f)]{
 
-Returns the sign of @racket[x] as either @math{-1}, @math{0}, or
-@math{1}.
+Returns the sign of @racket[x] as either @math{-1}, @math{0},
+@math{1}, or not-a-number.
 
 @mz-examples[
 #:eval math-eval
 (sgn 10)
 (sgn -10.0)
 (sgn 0)
+(sgn +nan.0)
 ]}
 
 @defproc[(conjugate [z number?]) number?]{