# [plt-scheme] fractions and decimals

Sorry, don't know where 1/90 came from, should of course be 11/10.
on 1/20/03 11:57 AM, Paul Schlie wrote:
>*
*>* 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_ == 11/10 ; 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_ == 11/10 ; 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
*>>>*
*