**Source code:** Lib/fractions.py

The fractions 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.

*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 instancesof numbers.Rational and returns a new Fraction instancewith value`numerator/denominator`

. If*denominator*is`0`

, itraises a ZeroDivisionError. The second version requires that*other_fraction*is an instance of numbers.Rational and returns aFraction instance with the same value. The next two versions accepteither a float or a decimal.Decimal instance, and return aFraction instance with exactly the same value. Note that due to theusual issues with binary floating-point (see Floating Point Arithmetic: Issues and Limitations), theargument 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 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 ofdecimal digits (underscores may be used to delimit digits as withintegral literals in code). In addition, any string that represents a finitevalue and is accepted by the float constructor is alsoaccepted by the Fraction constructor. In either form theinput 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 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 properties and methods:

Changed in version 3.2: The Fraction constructor now accepts float anddecimal.Decimal instances.

See Also0.142857 as a fractionChanged in version 3.9: The math.gcd() function is now used to normalize the

*numerator*and*denominator*. math.gcd() always return a int type.Previously, the GCD type depended on*numerator*and*denominator*.Changed in version 3.11: Underscores are now permitted when creating a Fraction instancefrom a string, following PEP 515 rules.

Changed in version 3.11: Fraction implements

`__int__`

now to satisfy`typing.SupportsInt`

instance checks.Changed in version 3.12: Space is allowed around the slash for string inputs:

`Fraction('2 / 3')`

.Changed in version 3.12: Fraction instances now support float-style formatting, withpresentation types

`"e"`

,`"E"`

,`"f"`

,`"F"`

,`"g"`

,`"G"`

and`"%""`

.- numerator¶
Numerator of the Fraction in lowest term.

- denominator¶
Denominator of the Fraction in lowest term.

- as_integer_ratio()¶
Return a tuple of two integers, whose ratio is equalto the original Fraction. The ratio is in lowest termsand has a positive denominator.

Added in version 3.8.

- is_integer()¶
Return

`True`

if the Fraction is an integer.Added in version 3.12.

*classmethod*from_float(*flt*)¶Alternative constructor which only accepts instances offloat or numbers.Integral. Beware that

`Fraction.from_float(0.3)`

is not the same value as`Fraction(3, 10)`

.Note

From Python 3.2 onwards, you can also construct aFraction instance directly from a float.

*classmethod*from_decimal(*dec*)¶Alternative constructor which only accepts instances ofdecimal.Decimal or numbers.Integral.

Note

From Python 3.2 onwards, you can also construct aFraction instance directly from a decimal.Decimalinstance.

- limit_denominator(
*max_denominator=1000000*)¶ Finds and returns the closest Fraction to

`self`

that hasdenominator at most max_denominator. This method is useful for findingrational 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)

- __floor__()¶
Returns the greatest int

`<= self`

. This method canalso be accessed through the math.floor() function:>>> from math import floor>>> floor(Fraction(355, 113))3

- __ceil__()¶
Returns the least int

`>= self`

. This method canalso be accessed through the math.ceil() function.

- __round__()¶
- __round__(
*ndigits*) The first version returns the nearest int to

`self`

,rounding half to even. The second version rounds`self`

to thenearest multiple of`Fraction(1, 10**ndigits)`

(logically, if`ndigits`

is negative), again rounding half toward even. Thismethod can also be accessed through the round() function.

- __format__(
*format_spec*,*/*)¶ Provides support for float-style formatting of Fractioninstances via the str.format() method, the format() built-infunction, or Formatted string literals. Thepresentation types

`"e"`

,`"E"`

,`"f"`

,`"F"`

,`"g"`

,`"G"`

and`"%"`

are supported. For these presentation types, formatting for aFraction object`x`

follows the rules outlined forthe float type in the Format Specification Mini-Language section.Here are some examples:

>>> from fractions import Fraction>>> format(Fraction(1, 7), '.40g')'0.1428571428571428571428571428571428571429'>>> format(Fraction('1234567.855'), '_.2f')'1_234_567.86'>>> f"{Fraction(355, 113):*>20.6e}"'********3.141593e+00'>>> old_price, new_price = 499, 672>>> "{:.2%} price increase".format(Fraction(new_price, old_price) - 1)'34.67% price increase'

See also

- Module numbers
The abstract base classes making up the numeric tower.