CODEWITHSUNDEEP
pythonpython-3.xfloating-pointfractions
itdxer
itdxer

Reputation: 1256

Python float to ratio

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)

Upvotes: 10

Views: 9595

Answers (3)

user2285236
user2285236

Reputation:

While using the fractions module, it is better to provide a string instead of a float to avoid floating point representation issues.

For example, if you pass '3.2' instead of 3.2 you get your desired result:

In : fractions.Fraction('3.2')
Out: Fraction(16, 5)

If you already have the value stored in a variable, you can use string formatting as well.

In : value = 3.2

In : fractions.Fraction(f'{value:.2f}')
Out: Fraction(16, 5)

Upvotes: 3

Martijn Pieters
Martijn Pieters

Reputation: 1122092

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.

Upvotes: 20

Jon Clements
Jon Clements

Reputation: 142156

It's not 16/5 because 3.2 isn't 3.2 exactly... it's a floating point rough approximation of it... eg: 3.20000000000000017764

Upvotes: 5

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