I try to represent a floating point number as a ratio of two integers, but for some reason the integers that I get are quite different from what I would expect to see. Can somebody explain this?
>>> value = 3.2
>>> ratios = value.as_integer_ratio()
>>> ratios
(3602879701896397, 1125899906842624)
>>> ratios[0] / ratios[1]
3.2
I would say that (32, 10) or (16, 5) are much better solutions to the problem. What's strange is that if I try to do the same for number like 2.5, the answer is exactly what I would expect
>>> value = 2.5
>>> value.as_integer_ratio()
(5, 2)
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
Fractiontoselfthat 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.