[plt-scheme] fractions and decimals
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-