# [Tutor] converting decimals to fractions

Blake.Garretson@dana.com Blake.Garretson@dana.com
Mon, 8 Oct 2001 14:37:12 -0400

```Thanks, Tim!  I have an uncanny knack for finding a brute force method even
if there is a more obvious and very elegant solution available.  Thanks for
the great code.

Blake Garretson

"Tim Peters"
<tim.one@home        To:     <Blake.Garretson@dana.com>, <tutor@python.org>
.com>                cc:
Subject:     RE: [Tutor] converting decimals to fractions
10/08/2001
01:47 PM

>def tofrac(x, largest_denominator=32):
>    """Return triple (i, j, k) where x ~= i + j/k.
>
>    x >= 0 is required.
>    i, j and k are integers >= 0, and k is > 0.
>    j and k have no factors in common, unless j is 0.
>
>    Optional argument largest_denominator (default 32) should be a
>    power of 2, and is the largest value k can have.
>    """
>
>    if not x >= 0:
>        raise ValueError("x must be >= 0")
>    scaled = int(round(x * largest_denominator))
>    whole, leftover = divmod(scaled, largest_denominator)
>    if leftover:
>        while leftover % 2 == 0:
>            leftover >>= 1
>            largest_denominator >>= 1
>    return whole, leftover, largest_denominator

```