:mod:`fractions` --- Rational numbers
Source code: :source:`Lib/fractions.py`
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: