On Fri, Oct 09, 2020 at 03:53:24AM +1100, Chris Angelico wrote:
> On Fri, Oct 9, 2020 at 3:43 AM Steven D'Aprano <st...@pearwood.info> wrote:
> >
> > On Thu, Oct 08, 2020 at 11:58:04AM -0400, Random832 wrote:
> >
> > > I was making a "convert Fraction to Decimal, exactly if possible"
> > > function and ran into a wall: it's not possible to do some of the
> > > necessary operations with exact precision in decimal:
> >
> > Of course you can't do them with *exact* precision in Decimal, because
> > that only has a fixed precision. (User-configurable, but fixed.)
> >
> >
> > py> from decimal import Decimal
> > py> from fractions import Fraction
> > py> x = Fraction(1, 3)
> > py> Decimal(x.numerator)/x.denominator
> > Decimal('0.3333333333333333333333333333')
> >
> >
>
> You trimmed off the part where the OP said that the denominator would
> be only multiples of 2 and/or 5 :)
I trimmed it because I didn't understand the relevance. If the
denominator is an exact multiple of only 2 and 5, then I think the
conversion will be exact if the precision is sufficient.
> >>> Fraction(1, 2) ** 53 * Fraction(1, 5) ** 47
> Fraction(1, 6400000000000000000000000000000000000000000000000)
> >>> Decimal("314159265358979323") / _.denominator
> Decimal('4.908738521234051921875E-32')
>
> In theory, this should be precisely representable in decimal, but how
> many digits would you need?
The brute force way of doing that will be to trap on Inexact and do the
division. If it succeeds, you are done; otherwise double the precision
and try again. Repeat until you either succeed, or reach the maximum
possible precision.
I don't know of any clever way of predicting the number of decimal
places a fraction will take as a decimal short of actually doing the
division. It does not depend on only the denominator, you also need to
know the numerator:
Decimal(1/4) # requires 2 decimal places
Decimal(2/4) # requires only 1 decimal place
--
Steve
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