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(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 newFraction
instance with valuenumerator/denominator
. If denominator is0
, it raises aZeroDivisionError
. The second version requires that other_fraction is an instance ofnumbers.Rational
and returns aFraction
instance with the same value. The next two versions accept either afloat
or adecimal.Decimal
instance, and return aFraction
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 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 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 return aint
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"%""
.- 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.
New in version 3.8.
- is_integer()¶
Return
True
if the Fraction is an integer.New 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 float-style formatting of
Fraction
instances via thestr.format()
method, theformat()
built-in function, or Formatted string literals. The presentation types"e"
,"E"
,"f"
,"F"
,"g"
,"G"
and"%"
are supported. For these presentation types, formatting for aFraction
objectx
follows the rules outlined for thefloat
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.