fractions

The fractions module provides the Fraction class for representing rational numbers exactly. Unlike floating-point numbers, Fraction objects represent numbers like 1/3 without any rounding error. This makes the module essential for financial calculations, precise measurements, and any scenario where decimal accuracy matters.

Syntax

from fractions import Fraction

# Create a fraction
Fraction(numerator=0, denominator=1)
Fraction(string)  # e.g., "3/7"
Fraction(float)
Fraction(decimal)

The Fraction Class

The Fraction class is the primary entry point. It can be constructed from integers, strings, floats, decimals, or another Fraction.

Parameters

Parameter	Type	Default	Description
numerator	int	0	The top number in the fraction
denominator	int	1	The bottom number (must not be zero)

Constructing from different types

from fractions import Fraction

# From integers
half = Fraction(1, 2)
print(half)
# 1/2

# From a float (exact representation)
point_one = Fraction(0.1)
print(point_one)
# 3602879701896397/36028797018963968

# From a string
three_sevenths = Fraction("3/7")
print(three_sevenths)
# 3/7

# From a decimal
exact = Fraction(Decimal("0.25"))
print(exact)
# 1/4

Fraction arithmetic

from fractions import Fraction

a = Fraction(1, 2)
b = Fraction(3, 4)

# All basic operations work
print(a + b)      # 5/4
print(a - b)      # -1/4
print(a * b)      # 3/8
print(a / b)      # 2/3

# Comparisons work too
print(a < b)      # True
print(a == b)     # False

Class Methods

Fraction.from_float()

Creates a Fraction from a floating-point number. This method converts the exact binary representation to a rational number.

from fractions import Fraction

# From float
result = Fraction.from_float(0.5)
print(result)
# 1/2

# Note: float representation is exact
result = Fraction.from_float(0.1)
print(result)
# 3602879701896397/36028797018963968

Fraction.from_decimal()

Creates a Fraction from a Decimal object. This is useful when working with decimal financial data.

from fractions import Fraction
from decimal import Decimal

# From decimal
result = Fraction.from_decimal(Decimal("0.25"))
print(result)
# 1/2

# Useful for money calculations
dollar = Fraction(Decimal("10.50"))
print(dollar)
# 21/2

The gcd() Function

The fractions module also exposes math.gcd() for computing the greatest common divisor of two integers.

from math import gcd

print(gcd(48, 18))
# 6

Common Patterns

Avoiding floating-point errors

from fractions import Fraction

# Instead of 0.1 + 0.2 (which gives 0.30000000000000004)
result = Fraction(1, 10) + Fraction(2, 10)
print(result == Fraction(3, 10))
# True

Working with repeating decimals

from fractions import Fraction

# 1/3 as a fraction
third = Fraction(1, 3)
print(third)
# 1/3

# Operations remain exact
print(third * 3)
# 1

Converting to other types

from fractions import Fraction

f = Fraction(5, 4)

print(float(f))      # 1.25
print(int(f))        # 1 (truncates)
print(f.numerator)   # 5
print(f.denominator) # 4

See Also

• datetime
• calendar
• time