diff --git a/pkgs/racket-test-core/tests/racket/math.rktl b/pkgs/racket-test-core/tests/racket/math.rktl
index fce2674b71..85e1bf459e 100644
--- a/pkgs/racket-test-core/tests/racket/math.rktl
+++ b/pkgs/racket-test-core/tests/racket/math.rktl
@@ -329,6 +329,7 @@
 (test 0 tanh 0)
 (test #t double=? tanh+1 (tanh 1))
 (test 1.0 tanh 20)
+(test #t flonum? (tanh (inexact->exact 1/100000000000)))
 
 #reader "maybe-single.rkt"
 (begin
diff --git a/racket/collects/racket/math.rkt b/racket/collects/racket/math.rkt
index 2f470151ad..50a0919ddc 100644
--- a/racket/collects/racket/math.rkt
+++ b/racket/collects/racket/math.rkt
@@ -73,7 +73,7 @@
           [(real? z)
            (let loop ([z z])
              (cond [(z . < . 0)   (- (loop (- z)))]
-                   [(z . < . 1.29047841397589243466D-08) z]
+                   [(z . < . 1.29047841397589243466D-08) (exact->inexact z)]
                    [(z . < . 0.54930614433405484570D+00)
                     (define p0 -0.16134119023996228053D+04)
                     (define p1 -0.99225929672236083313D+02)