on floating-point numbers

[Chris Angelico]

On Sun, Sep 5, 2021 at 12:58 PM Greg Ewing <greg.ewing at canterbury.ac.nz> wrote:
>
> On 5/09/21 2:42 am, Hope Rouselle wrote:
> > Here's what I did on this case.  The REPL is telling me that
> >
> >    7.23 = 2035064081618043/281474976710656
>
> If 7.23 were exactly representable, you would have got
> 723/1000.
>
> Contrast this with something that *is* exactly representable:
>
>  >>> 7.875.as_integer_ratio()
> (63, 8)
>
> and observe that 7875/1000 == 63/8:
>
>  >>> from fractions import Fraction
>  >>> Fraction(7875,1000)
> Fraction(63, 8)
>
> In general, to find out whether a decimal number is exactly
> representable in binary, represent it as a ratio of integers
> where the denominator is a power of 10, reduce that to lowest
> terms, and compare with the result of as_integer_ratio().
>

Or let Python do that work for you!

>>> from fractions import Fraction
>>> Fraction("7.875") == Fraction(7.875)
True
>>> Fraction("7.8") == Fraction(7.8)
False

ChrisA