what's the precision of fractions.Fraction?

[RJB]

Does Fractions remove common factors the way it should?

If it does and you want to find the closest fraction with a smaller
denominator i think tou'll need some number theory and continued
fractions.

RJB
On Nov 18, 8:26 pm, Steven D'Aprano <st... at REMOVE-THIS-
cybersource.com.au> wrote:
> On Thu, 18 Nov 2010 20:08:00 +0100, Stefan Sonnenberg-Carstens wrote:
> > If you need it really *precise*, cast your Fractions into type Decimal:
>
> It's actually the opposite. Decimal has many advantages, but being
> "really precise" is not one of them. It suffers the exact same issues re
> precision and round-off as binary floating point.
>
> It is easy to demonstrate that there are numbers which cannot be
> represented precisely as Decimals no matter how many decimal places you
> use, but can be represented exactly as Fractions. Fraction can exactly
> represent every Decimal, but Decimal cannot represent exactly every
> Fraction.
>
> We're not talking about weird edge cases either, but simple numbers that
> you're likely to come across every day:
>
> >>> from decimal import Decimal
> >>> one_ninth = Decimal(1)/Decimal(9)
> >>> two_thirds = Decimal(2)/Decimal(3)
> >>> one_ninth*6 == two_thirds
>
> False
>
> >>> from fractions import Fraction
> >>> one_ninth = Fraction(1, 9)
> >>> two_thirds = Fraction(2, 3)
> >>> one_ninth*6 == two_thirds
>
> True
>
> Still not convinced?
>
> >>> f = Fraction(1) + Fraction(1, 10**100000)
> >>> f != 1
>
> True
>
> (which is virtually instantaneous, by the way)
>
> compared to the *much* slower:
>
> >>> d = Decimal(1) + Decimal(1)/Decimal(10**100000)
> >>> d != 1
>
> False
>
> Yes, I could try to set the Decimal context to 100,000 decimal places --
> and just as easily defeat it again by adding one more to the exponent.
>
> In my opinion, the Fraction module is one of the least appreciated and
> underused modules in the standard library -- and I include myself in
> that. It really is a joy, and I don't use it anywhere near enough.
>
> --
> Steven