# [plt-scheme] fractions and decimals

with a few more as *annotations:
on 1/20/03 11:05 AM, Paul Schlie wrote:
>*
*>* Your understanding of was correct, the converse isn't bad either,
*>* maybe better:
*>*
*>* A) zero(0) and repeat(_) terminated decimal fractions being exact,
*>* inexact otherwise:
*>*
*>* 1 == 1 ; exact
*>* 1. == 1. ; inexact
*>* 1.0 == 1 ; exact
** 1.0_ == 1 ; exact (0 repeat redundant, but consistent)
>* 1.1 == 1.1 ; inexact
*>* 1.1_ == 10/9 ; exact
*>* 1.10 == 11/10 ; exact
** 1.10_ ~ 101/91 ; exact (10 repeat remains exact)
* 1.1_0_ == 1/90 ; exact ( 0 repeat redundant, but consistent)
>*
*>* vs.
*>*
*>* B) non-zero(1-9) and repeat(_) terminated decimal fractions being exact,
*>* inexact otherwise:
*>*
*>* 1 == 1 ; exact
*>* 1. == 1. ; inexact
*>* 1.0 == 1.0 ; inexact
** 1.0_ == 1 ; exact (0 repeat transforms inexact -> exact)
>* 1.1 == 11/10 ; exact
*>* 1.1_ == 10/9 ; exact
*>* 1.10 == 1.10 ; inexact
** 1.10_ ~ 101/91 ; exact (10 repeat transforms inexact -> exact)
* 1.1_0_ == 1/90 ; exact ( 0 repeat transforms inexact -> exact)
>*
*>* Option A does seem arguably more reasonable,
*>*
*>* -paul-
*>*
*>* on 1/20/03 10:11 AM, Matthew Flatt wrote:
*>>*
*>>* At Sun, 19 Jan 2003 21:00:23 -0500, Paul Schlie wrote:
*>>>* Wonder if broadly adopting the convention that decimals terminated with a
*>>>* zero (0), would be interpreted as an inexact number, otherwise considered
*>>>* exact; would help unify the two worlds;
*>>*
*>>* I may be misunderstanding the proposal, but I don't think this would
*>>* solve the problem for the teaching levels. For example, when working
*>>* with American dollars, students expect "0.10" to mean exactly a dime.
*>>*
*>>* Matthew
*>>*
*