9.5.fractions — Rational numbers¶

Source code:Lib/fractions.py

Thefractions module provides support for rational number arithmetic.

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

classfractions.Fraction(numerator=0,denominator=1)¶

classfractions.Fraction(other_fraction)

classfractions.Fraction(float)

classfractions.Fraction(decimal)

classfractions.Fraction(string)

The first version requires thatnumerator anddenominator are instancesofnumbers.Rational and returns a newFraction instancewith valuenumerator/denominator. Ifdenominator is0, itraises aZeroDivisionError. The second version requires thatother_fraction is an instance ofnumbers.Rational and returns aFraction instance with the same value. The next two versions accepteither afloat or adecimal.Decimal instance, and return aFraction instance with exactly the same value. Note that due to theusual issues with binary floating-point (seeFloating Point Arithmetic: Issues and Limitations), theargument toFraction(1.1) is not exactly equal to 11/10, and soFraction(1.1) doesnot returnFraction(11,10) as one might expect.(But see the documentation for thelimit_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 optionalsign may be either ‘+’ or ‘-‘ andnumerator anddenominator (if present) are strings ofdecimal digits. In addition, any string that represents a finitevalue and is accepted by thefloat constructor is alsoaccepted by theFraction constructor. In either form theinput string may also have leading and/or trailing whitespace.Here are some examples:

>>>fromfractionsimportFraction>>>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)>>>fromdecimalimportDecimal>>>Fraction(Decimal('1.1'))Fraction(11, 10)

TheFraction class inherits from the abstract base classnumbers.Rational, and implements all of the methods andoperations 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:TheFraction constructor now acceptsfloat anddecimal.Decimal instances.

from_float(flt)¶

This class method constructs aFraction representing the exactvalue offlt, which must be afloat. Beware thatFraction.from_float(0.3) is not the same value asFraction(3,10).

Note

From Python 2.7 onwards, you can also construct aFraction instance directly from afloat.

from_decimal(dec)¶

This class method constructs aFraction representing the exactvalue ofdec, which must be adecimal.Decimal.

Note

From Python 2.7 onwards, you can also construct aFraction instance directly from adecimal.Decimalinstance.

limit_denominator(max_denominator=1000000)¶

Finds and returns the closestFraction toself that hasdenominator at most max_denominator. This method is useful for findingrational approximations to a given floating-point number:

>>>fromfractionsimportFraction>>>Fraction('3.1415926535897932').limit_denominator(1000)Fraction(355, 113)

or for recovering a rational number that’s represented as a float:

>>>frommathimportpi,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 integersa andb. If eithera orb is nonzero, then the absolute value ofgcd(a,b) is thelargest integer that divides botha andb.gcd(a,b) has the samesign asb ifb is nonzero; otherwise it takes the sign ofa.gcd(0,0) returns0.