# [plt-scheme] fractions and decimals

>* I'm playing with the new "test suite" feature, and was surprised to
*>* discover that (cube 1/2) is NOT 0.125 (although it DOES match 1/8).
*>* On further investigation, I found that (equal? 0.125 1/8) returns true
*>* in Beginner mode, but #f in R5RS and textual mzscheme. Whazzap?
*
Scheme has a notion of "exactness" of numbers:
http://download.plt-scheme.org/doc/r5rs/r5rs-Z-H-9.html#%_sec_6.2.2
If I understand correctly... the decimal-point literal "0.125" is
assumed "inexact" by default (I think for historical/performance
reasons, so that an implementation can use inexact native floating-point
numbers and operations unless the programmer directs otherwise). The
ratio literal "1/8" is assumed "exact":
(exact? 0.125) => #f
(exact? 1/8) => #t
You can use the "#e" prefix for expressing exact constants as
decimal-point literals, and you can use the "inexact->exact" procedure
to create an exact value from an inexact one:
(equal? 0.125 1/8) => #f
(equal? #e0.125 1/8) => #t
(equal? (inexact->exact 0.125) 1/8) => #t
If your computations don't require exactness, you can use "#e" and
"inexact->exact" with impunity. You may still have difficulty testing
the equality of two rational numbers, due to floating-point lossiness.
(I defer to the mathematician on any philosophical implications.)
--
http://www.neilvandyke.org/