# [plt-scheme] fractions and decimals

 From: Paul Schlie (schlie at attbi.com) Date: Mon Jan 20 12:25:53 EST 2003 Previous message: [plt-scheme] fractions and decimals Next message: [plt-scheme] MzLib's unitsig.ss Messages sorted by: [date] [thread] [subject] [author]

```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:
>>
>> 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
>>>

```

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