# [racket] Decimal rounding problem

On 11/29/2012 11:06 AM, Stephen Bloch wrote:
>*
*>* On Nov 29, 2012, at 9:44 AM, Greg Graham wrote:
*>*
*>>* I am trying to report GPA calculation results to 2 decimal places, so I thought real->decimal-string would do the trick. However, the following behavior surprised me:
*>>*
*>>>* (real->decimal-string 3.225 2)
*>>* "3.23"
*>>>* (real->decimal-string 4.225 2)
*>>* "4.22"
*>>*
*>>* I would like the second answer to be "4.23", which is what a student would expect to see if they did the calculations themselves. The documentation for real->decimal-string says that it first converts the argument to an exact number. I suspect the problem has something to do with this:
*>>*
*>>>* (inexact->exact 4.225)
*>>* 4 126663739519795/562949953421312
*>>>* (/ 126663739519795.0 562949953421312.0)
*>>* 0.22499999999999964
*>>*
*>>* Is there another rounding function that would just round the floating point without going through the conversion to exact?
*>*
*>* Another rounding function won't help, because by the time the READER has finished with the character string "4.225", the internal form is already slightly less than 4225/1000. And if you're getting the inexact 4.225 from somewhere else, again it's not really 4225/1000 so it's already too late to round it the way you want.
*>*
*>* You could work in a student language, where the reader reads decimals as exact by default :-)
*>*
*>* Seriously, I'm sure there's a way to tell the reader in other languages to read decimals as exact; I just don't know what it is.
*
Prefix the number with "#e", as in
> #e4.225
169/40
As an alternative, you could create a language that sets the
'read-decimal-as-inexact' reader parameter to #f before reading the
module contents. Try saving the following as s-exp-exact/lang/reader.rkt
(adapted from s-exp/lang/reader.rkt with some help from Carl):
(module reader syntax/module-reader
#:language (lambda (p) (read-syntax (object-name p) p))
#:wrapper1 (lambda (go)
(parameterize ((read-decimal-as-inexact #f)) (go))))
Then run
#lang s-exp-exact racket
(exact? 4.225)
Ryan