# [PD] number to fractions external?

Ludwig Maes ludwig.maes at gmail.com
Fri Dec 16 19:00:20 CET 2011

```If you guys 'd done your math, you'd know there is an ancient algorithm for
approximating numbers by fractions and its called continued fractions.

On 16 December 2011 18:38, Lorenzo Sutton <lorenzofsutton at gmail.com> wrote:

> On 16/12/11 16:05, Alexandre Torres Porres wrote:
>
>> looks like a job for an external
>>
> Not really answering the OP question but something could be done in Python:
>
> def find_frac(num):
>    f = float(num)
>    last_error = 1000
>    best = (0,0)
>    for i in xrange(1,1001):
>        for j in xrange(1,i+1):
>            divide = (float(i) / float (j))
>            if divide == f:
>                return ((i,j),0)
>            err = abs(divide - f)
>            if err < last_error:
>                best = (i,j)
>                last_error = err
>    return (best,last_error)
>
> This would try to find the exact fraction or the one with the smallest
> error (trying up to 1000/1000). It would return (numerator, denominator,
> error). Guess it would work well at least up to 100 but only for positive
> numbers... and... not for numbers < 1.. and surely it's not optimised etc.
> etc. :)
>
> >>> find_frac(2)
> ((2, 1), 0)
> >>> find_frac(1.5)
> ((3, 2), 0)
> >>> find_frac(1.**333333333333333333333333333)
> ((4, 3), 0)
> >>> find_frac(2.4)
> ((12, 5), 0)
> >>> find_frac(2.8)
> ((14, 5), 0)
> >>> find_frac(2.987654321)
> ((242, 81), 1.234568003383174e-11)
> >>> find_frac(50.32)
> ((956, 19), 0.004210526315787888)
> >>> find_frac(50.322)
> ((956, 19), 0.006210526315790332)
> >>> find_frac(50.4)
> ((252, 5), 0)
> >>> find_frac(10.33)
> ((971, 94), 0.00021276595744623705)
> >>> find_frac(10.**33333333333333333333333333)
> ((31, 3), 0)
>
> Lorenzo.
>
>>
>>
>>
>> 2011/12/16 i go bananas <hard.off at gmail.com <mailto:hard.off at gmail.com>>
>>
>>
>>    actually, i'm not going to do anything more on this.
>>
>>    i had a look at the articles claude posted, and they went a bit
>>    far over my head.
>>
>>    my patch will still work for basic things like 1/4 and 7/8, but i
>>    wouldn't depend on it working for a serious application.  As you
>>    first suggested, it's not so simple, and if you read claude's
>>    articles, you will see that it isn't.
>>
>>    it's not brain science though, so maybe someone with a bit more
>>    number understanding can tackle it.
>>
>>
>>
>>    On Sat, Dec 17, 2011 at 12:51 AM, Alexandre Torres Porres
>>    <porres at gmail.com <mailto:porres at gmail.com>> wrote:
>>
>>        > i had a go at it
>>
>>        thanks, I kinda had to go too, but no time... :(
>>
>>        > yeah, my patch only works for rational numbers.
>>
>>        you know what, I think I asked this before on this list,
>>
>>        deja'vu
>>
>>        > will have a look at the article / method you posted, claude.
>>
>>        are you going at it too? :)
>>
>>        by the way, I meant something like 1.75 becomes 7/4 and not
>>        3/4, but that is easy to adapt on your patch
>>
>>        thanks
>>
>>        cheers
>>
>>
>>
>>        2011/12/16 i go bananas <hard.off at gmail.com
>>        <mailto:hard.off at gmail.com>>
>>
>>
>>            by the way, here is the method i used:
>>
>>            first, convert the decimal part to a fraction in the form
>>            of n/100000
>>            next, find the highest common factor of n and 100000
>>            (using the 'division method' like this:
>>            http://easycalculation.com/**what-is-hcf.php<http://easycalculation.com/what-is-hcf.php>)
>>
>>            then just divide n and 100000 by that factor.
>>
>>            actually, that means it's accurate to 6 decimal places, i
>>            guess.  well...whatever :D
>>
>>
>>
>>
>>
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>
>
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