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:mod:`fractions` --- Rational numbers

Source code: :source:`Lib/`

The :mod:`fractions` module provides support for rational number arithmetic.

A Fraction instance can be constructed from a pair of integers, from another rational number, or from a string.

The first version requires that numerator and denominator are instances of :class:`numbers.Rational` and returns a new :class:`Fraction` instance with value numerator/denominator. If denominator is :const:`0`, it raises a :exc:`ZeroDivisionError`. The second version requires that other_fraction is an instance of :class:`numbers.Rational` and returns a :class:`Fraction` instance with the same value. The next two versions accept either a :class:`float` or a :class:`decimal.Decimal` instance, and return a :class:`Fraction` instance with exactly the same value. Note that due to the usual issues with binary floating-point (see :ref:`tut-fp-issues`), the argument to Fraction(1.1) is not exactly equal to 11/10, and so Fraction(1.1) does not return Fraction(11, 10) as one might expect. (But see the documentation for the :meth:`limit_denominator` method below.) The last version of the constructor expects a string or unicode instance. The usual form for this instance is:

[sign] numerator ['/' denominator]

where the optional sign may be either '+' or '-' and numerator and denominator (if present) are strings of decimal digits. In addition, any string that represents a finite value and is accepted by the :class:`float` constructor is also accepted by the :class:`Fraction` constructor. In either form the input string may also have leading and/or trailing whitespace. Here are some examples:

>>> from fractions import Fraction
>>> Fraction(16, -10)
Fraction(-8, 5)
>>> Fraction(123)
Fraction(123, 1)
>>> Fraction()
Fraction(0, 1)
>>> Fraction('3/7')
Fraction(3, 7)
>>> Fraction(' -3/7 ')
Fraction(-3, 7)
>>> Fraction('1.414213 \t\n')
Fraction(1414213, 1000000)
>>> Fraction('-.125')
Fraction(-1, 8)
>>> Fraction('7e-6')
Fraction(7, 1000000)
>>> Fraction(2.25)
Fraction(9, 4)
>>> Fraction(1.1)
Fraction(2476979795053773, 2251799813685248)
>>> from decimal import Decimal
>>> Fraction(Decimal('1.1'))
Fraction(11, 10)

The :class:`Fraction` class inherits from the abstract base class :class:`numbers.Rational`, and implements all of the methods and operations from that class. :class:`Fraction` instances are hashable, and should be treated as immutable. In addition, :class:`Fraction` has the following methods: