[plt-scheme] fractions and decimals

How about using "_" to denote the range of repeating digits in
lieu of the previously suggested "..", like possibly the following:

0.0000_142857_ (which is closer to the notion of an over-bar)

Actually it would be nice to generally allow "_" to denote the visual
separation of digits; where if the number is terminated with a "_",
then the digits between the most previous "." or "_" are repeated; and
other occurrences of "_" are simply ignored, or inserted if desired
as on output format preference at every N digits of significance.
(where 3 for decimal, 4 for hex/binary, etc. may make sense, as
 numbers with many digits of significance are hard to read and write.)

1/3    == 0.3_
1/30   == 0.0_3_
1/300  == 0.00_3_
1/700  == 0.00_142857_

With "_" used as a visual separator with a terminating repeat:

123_456_789/700 == 176_366.84_142857_

(actually kind of like this better than the earlier suggested baby ellipse)

-paul-

on 1/19/03 9:38 PM, Robert Bruce Findler wrote:
>
> I must say (not being the one to implement it :) that I really like the
> idea of useing ... to indicate the overbar in DrScheme, but how do you
> notate those rationals whose expansion includes multiple repeated
> digits, like 1/70000:
> 
> 0.0000142857
>   ^^^^        nonrepeating
>       ^^^^^^  repeating
> 
> Robby
> 
> At Sun, 19 Jan 2003 21:00:23 -0500, Paul Schlie wrote:
>>   For list-related administrative tasks:
>>   http://list.cs.brown.edu/mailman/listinfo/plt-scheme
>> 
>> 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; (little fancier would be to
>> interpret ".." as an exact repeating input pattern, although not sure how
>> to reliably convert it into an exact fractional internal representation.
>> 
>> 1      == 1      ; exact
>> 1.0    == 1.0    ; inexact
>> 
>> 0.125  == 1/8    ; exact
>> 0.1250 == 0.1250 ; inexact
>> 
>> 0.3..  == 1/3    ; exact
>> 0.33   == 33/100 ; exact
>> 0.3330 == 0.3330 ; inexact
>> 
>> Such if decimal outputs are specified as being preferred:
>> 
>> 1/8    => 0.125  ; exact to the specified decimal precision.
>> 0.125  => 0.125  ; exact to the specified decimal precision.
>> 0.1250 => 0.1250 ; inexact to the specified decimal precision.
>> 
>> 1/3    => 0.3..  ; exact to the specified decimal precision.
>> 0.33   => 0.33   ; exact to the specified decimal precision.
>> 0.3330 => 0.3330 ; inexact to the specified decimal precision.
>> 
>> Or if fractional output were specified as being preferred:
>> 
>> 1/8    => 1/8    ; exact to the specified decimal precision.
>> 0.125  => 1/8    ; exact to the specified decimal precision.
>> 0.1250 => 0.1250 ; inexact to the specified decimal precision.
>> 
>> 1/3    => 1/3    ; exact to the specified decimal precision.
>> 0.3..  => 1/3    ; exact to the specified decimal precision.
>> 0.33   => 33/100 ; exact to the specified decimal precision.
>> 0.3330 => 0.3330 ; inexact to the specified decimal precision.
>> 
>> (where ".." would be replaced with an over-bar within DrScheme, but
>>  copied to the clipboard as "..", to enable a successive pastes)
>> 
>> Which overall seems reasonably nice and simple,
>> 
>> -paul-
>