# [plt-scheme] fractions and decimals

 From: Paul Schlie (schlie at attbi.com) Date: Mon Jan 20 11:57:50 EST 2003 Previous message: [plt-scheme] fractions and decimals Next message: [plt-scheme] fractions and decimals Messages sorted by: [date] [thread] [subject] [author]

```with a few more as *annotations:

on 1/20/03 11:05 AM, Paul Schlie wrote:
>
> 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
>>

```

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