Fractions (rational numbers) in Python

In Python, you can handle fractions (rational numbers) with the fractions module.

• fractions — Rational numbers — Python 3.11.4 documentation

See the following article on how to find the greatest common divisor and least common multiple.

• Find GCD and LCM in Python (math.gcd(), lcm())

All sample code in this article assumes that the Fraction class has been imported as follows:

from fractions import Fraction

Create a Fraction object

This section describes how to create a Fraction object with the constructor, Fraction(). In all cases, the result is automatically reduced (simplified).

Specify numerator and denominator as integers

You can specify the numerator and denominator as integers (int). The denominator is considered 1 if omitted.

print(Fraction(1, 3))
# 1/3

print(Fraction(2, 6))
# 1/3

print(Fraction(3))
# 3

Convert float to Fraction

If a floating-point number (float) is passed, it is converted to a Fraction.

print(Fraction(0.25))
# 1/4

print(Fraction(0.3333333333333333))
# 6004799503160661/18014398509481984

print(Fraction(0.3333333333333333).limit_denominator())
# 1/3

The limit_denominator() method can be used to limit the maximum value of the denominator. Details are provided later in this article.

Convert str to Fraction

If a string (str) in fractional notation is passed, it is converted to Fraction.

print(Fraction('2/5'))
# 2/5

print(Fraction('16/48'))
# 1/3

Get numerator and denominator

You can get the numerator and denominator with the numerator and denominator attributes of Fraction. These attributes are read-only and cannot be modified.

a = Fraction(1, 3)
print(a)
# 1/3

print(a.numerator)
print(type(a.numerator))
# 1
# <class 'int'>

print(a.denominator)
print(type(a.denominator))
# 3
# <class 'int'>

# a.numerator = 7
# AttributeError: property 'numerator' of 'Fraction' object has no setter

Calculate and compare fractions

You can perform calculations on Fraction objects using arithmetic operators.

• Arithmetic operators in Python (+, -, , /, //, %, *)

print(Fraction(1, 2) + Fraction(1, 3))
# 5/6

print(Fraction(1, 2) / Fraction(1, 3))
# 3/2

print(Fraction(1, 6) ** 2 + Fraction(1, 2) * Fraction(1, 3))
# 7/36

You can also use comparison operators with Fraction objects.

print(Fraction(7, 13) > Fraction(8, 15))
# True

Convert Fraction to float

You can convert Fraction to a floating-point number (float) with float().

print(float(Fraction(1, 5)))
# 0.2

The result of an operation between Fraction and float is automatically converted to float.

print(Fraction(1, 5) * 0.5)
# 0.1

Convert Fraction to str

You can convert Fraction to a string (str) with str().

print(str(Fraction(1, 3)))
# 1/3

print(type(str(Fraction(1, 3))))
# <class 'str'>

Get rational approximations: limit_denominator()

You can get a rational approximation with the limit_denominator() method.

• fractions.Fraction.limit_denominator() — Rational numbers — Python 3.11.4 documentation

The limit_denominator() method returns Fraction whose denominator is less than or equal to the max_denominator argument. The default is max_denominator=1000000.

Approximate Pi and Euler's number e

pi = Fraction(3.14159265359)
print(pi)
# 3537118876014453/1125899906842624

print(pi.limit_denominator(10))
print(pi.limit_denominator(100))
print(pi.limit_denominator(1000))
# 22/7
# 311/99
# 355/113

e = Fraction(2.71828182846)
print(e)
# 6121026514870223/2251799813685248

print(e.limit_denominator(10))
print(e.limit_denominator(100))
print(e.limit_denominator(1000))
# 19/7
# 193/71
# 1457/536

Convert repeating decimals to fractions

a = Fraction(0.3333333333333333)
print(a)
# 6004799503160661/18014398509481984

print(a.limit_denominator())
# 1/3

a = Fraction(0.14285714285714285)
print(a)
# 2573485501354569/18014398509481984

print(a.limit_denominator())
# 1/7