9.5. fractions — Rational numbers — Python documentation
9.5. fractions — Rational numbers
New in version 2.6.
Source code: :source:`Lib/fractions.py`
The 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.
- class fractions.Fraction(numerator=0, denominator=1)
class fractions.Fraction(other_fraction)
class fractions.Fraction(float)
class fractions.Fraction(decimal)
class fractions.Fraction(string) The first version requires that numerator and denominator are instances of numbers.Rational and returns a new Fraction instance with value
numerator/denominator
. If denominator is0
, it raises aZeroDivisionError
. The second version requires that other_fraction is an instance of numbers.Rational and returns a Fraction instance with the same value. The next two versions accept either a float or a decimal.Decimal instance, and return a Fraction instance with exactly the same value. Note that due to the usual issues with binary floating-point (see Floating Point Arithmetic: Issues and Limitations), the argument toFraction(1.1)
is not exactly equal to 11/10, and soFraction(1.1)
does not returnFraction(11, 10)
as one might expect. (But see the documentation for the 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 ‘-’ andnumerator
anddenominator
(if present) are strings of decimal digits. In addition, any string that represents a finite value and is accepted by the float constructor is also accepted by the 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 Fraction class inherits from the abstract base class numbers.Rational, and implements all of the methods and operations from that class. Fraction instances are hashable, and should be treated as immutable. In addition, Fraction has the following methods:
Changed in version 2.7: The Fraction constructor now accepts float and decimal.Decimal instances.
- from_float(flt)
This class method constructs a Fraction representing the exact value of flt, which must be a float. Beware that
Fraction.from_float(0.3)
is not the same value asFraction(3, 10)
.
- from_decimal(dec)
This class method constructs a Fraction representing the exact value of dec, which must be a decimal.Decimal.
Note
From Python 2.7 onwards, you can also construct a Fraction instance directly from a decimal.Decimal instance.
- limit_denominator(max_denominator=1000000)
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:>>> from fractions import Fraction >>> Fraction('3.1415926535897932').limit_denominator(1000) Fraction(355, 113)
or for recovering a rational number that’s represented as a float:
>>> from math import pi, cos >>> Fraction(cos(pi/3)) Fraction(4503599627370497, 9007199254740992) >>> Fraction(cos(pi/3)).limit_denominator() Fraction(1, 2) >>> Fraction(1.1).limit_denominator() Fraction(11, 10)
- fractions.gcd(a, b)
- Return the greatest common divisor of the integers a and b. If either a or b is nonzero, then the absolute value of
gcd(a, b)
is the largest integer that divides both a and b.gcd(a,b)
has the same sign as b if b is nonzero; otherwise it takes the sign of a.gcd(0, 0)
returns0
.