[plt-scheme] question about Scheme numbers

On May 12, 2006, at 10:21 PM, Peter Horst wrote:

> OK, so I've got (under Dr. Scheme 3.01 "Textual"):
>
> (define square
>  (lambda (n)
>    (* n n)))
>
> (define hypotenuse
>  (lambda (adjacent opposite)
>    (sqrt (+ (square adjacent) (square opposite)))))
>
> Calculating the hypotenuse of a 30-60-90 right triangle I get:
>
> > (hypo (sqrt 3) 1)
> 2.0
>
> but
>
> > (square (sqrt 3))
> 2.9999999999999996
>
> How come?
>
> Thank you!

Functions like this show how whole numbers add to other numbers that 
are not quite whole:

(define (add-x-to-nearly-3 x)
   (+ x 2.9999999999999996))

(map add-x-to-nearly-3
      '(-1000 -100 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1.0 2.0 3 4 5 10 100 
1000))

Results could depend a little on the computer:

(-997.0
  -97.0
  -7.0
  -6.0
  -5.0
  -4.0
  -3.0000000000000004
  -2.0000000000000004
  -1.0000000000000004
  -4.440892098500626e-16
  0.9999999999999996
  1.9999999999999996
  2.9999999999999996
  3.9999999999999996
  5.0
  6.0
  7.0
  8.0
  13.0
  103.0
  1003.0)

The effect is only noticeable on results near zero (for reasons that 
others have given.)

rac