on floating-point numbers

[Hope Rouselle]

Greg Ewing <greg.ewing at canterbury.ac.nz> writes:

> 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().

That makes perfect sense and answers my question.  I appreciate it.