floating point - Python float to ratio

Question

I try get ration of variable and get unexpected result. Can somebody explain this?

>>> value = 3.2
>>> ratios = value.as_integer_ratio()
>>> ratios
(3602879701896397, 1125899906842624)
>>> ratios[0] / ratios[1]
3.2

I using python 3.3

But I think that (16, 5) is much better solution

And why it correct for 2.5

>>> value = 2.5
>>> value.as_integer_ratio()
(5, 2)

Answer 1

Use the fractions module to simplify fractions:

>>> from fractions import Fraction
>>> Fraction(3.2)
Fraction(3602879701896397, 1125899906842624)
>>> Fraction(3.2).limit_denominator()
Fraction(16, 5)

From the Fraction.limit_denominator() function:

Finds and returns the closest Fraction to self that has denominator at most max_denominator. This method is useful for finding rational approximations to a given floating-point number

Floating point numbers are limited in precision and cannot represent many numbers exactly; what you see is a rounded representation, but the real number is:

>>> format(3.2, '.50f')
'3.20000000000000017763568394002504646778106689453125'

because a floating point number is represented as a sum of binary fractions; 1/5 can only be represented by adding up 1/8 + 1/16 + 1/128 + more binary fractions for increasing exponents of two.