fractions
— Rational numbers¶
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, from another rational number, or from a string.
- class fractions.Fraction(numerator=0, denominator=1)¶
- class fractions.Fraction(number)
- class fractions.Fraction(string)
The first version requires that numerator and denominator are instances of
numbers.Rational
and returns a newFraction
instance with valuenumerator/denominator
. If denominator is0
, it raises aZeroDivisionError
.The second version requires that number is an instance of
numbers.Rational
or has theas_integer_ratio()
method (this includesfloat
anddecimal.Decimal
). It returns aFraction
instance with exactly the same value. Assumed, that theas_integer_ratio()
method returns a pair of coprime integers and last one is positive. Note that due to the usual issues with binary 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 thelimit_denominator()
method below.)The last version of the constructor expects a string. 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 (underscores may be used to delimit digits as with integral literals in code). In addition, any string that represents a finite value and is accepted by thefloat
constructor is also accepted by theFraction
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 classnumbers.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 properties and methods:Changed in version 3.2: The
Fraction
constructor now acceptsfloat
anddecimal.Decimal
instances.Changed in version 3.9: The
math.gcd()
function is now used to normalize the numerator and denominator.math.gcd()
always returns anint
type. Previously, the GCD type depended on numerator and denominator.Changed in version 3.11: Underscores are now permitted when creating a
Fraction
instance from a string, following PEP 515 rules.Changed in version 3.11:
Fraction
implements__int__
now to satisfytyping.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, with presentation types"e"
,"E"
,"f"
,"F"
,"g"
,"G"
and"%""
.Changed in version 3.13: Formatting of
Fraction
instances without a presentation type now supports fill, alignment, sign handling, minimum width and grouping.Changed in version 3.14: The
Fraction
constructor now accepts any objects with theas_integer_ratio()
method.- 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 equal to the original Fraction. The ratio is in lowest terms and 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 of
float
ornumbers.Integral
. Beware thatFraction.from_float(0.3)
is not the same value asFraction(3, 10)
.
- classmethod from_decimal(dec)¶
Alternative constructor which only accepts instances of
decimal.Decimal
ornumbers.Integral
.Note
From Python 3.2 onwards, you can also construct a
Fraction
instance directly from adecimal.Decimal
instance.
- limit_denominator(max_denominator=1000000)¶
Finds and returns the closest
Fraction
toself
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)
- __floor__()¶
Returns the greatest
int
<= self
. This method can also be accessed through themath.floor()
function:>>> from math import floor >>> floor(Fraction(355, 113)) 3
- __ceil__()¶
Returns the least
int
>= self
. This method can also be accessed through themath.ceil()
function.
- __round__()¶
- __round__(ndigits)
The first version returns the nearest
int
toself
, rounding half to even. The second version roundsself
to the nearest multiple ofFraction(1, 10**ndigits)
(logically, ifndigits
is negative), again rounding half toward even. This method can also be accessed through theround()
function.
- __format__(format_spec, /)¶
Provides support for formatting of
Fraction
instances via thestr.format()
method, theformat()
built-in function, or Formatted string literals.If the
format_spec
format specification string does not end with one of the presentation types'e'
,'E'
,'f'
,'F'
,'g'
,'G'
or'%'
then formatting follows the general rules for fill, alignment, sign handling, minimum width, and grouping as described in the format specification mini-language. The “alternate form” flag'#'
is supported: if present, it forces the output string to always include an explicit denominator, even when the value being formatted is an exact integer. The zero-fill flag'0'
is not supported.If the
format_spec
format specification string ends with one of the presentation types'e'
,'E'
,'f'
,'F'
,'g'
,'G'
or'%'
then formatting follows the rules outlined for thefloat
type in the Format Specification Mini-Language section.Here are some examples:
>>> from fractions import Fraction >>> format(Fraction(103993, 33102), '_') '103_993/33_102' >>> format(Fraction(1, 7), '.^+10') '...+1/7...' >>> format(Fraction(3, 1), '') '3' >>> format(Fraction(3, 1), '#') '3/1' >>> 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.