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.Rationaland returns a new- Fractioninstance with value- numerator/denominator. If denominator is- 0, it raises a- ZeroDivisionError. The second version requires that other_fraction is an instance of- numbers.Rationaland returns a- Fractioninstance with the same value. The next two versions accept either a- floator a- decimal.Decimalinstance, and return a- Fractioninstance 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 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 - signmay be either ‘+’ or ‘-’ and- numeratorand- denominator(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 the- floatconstructor is also accepted by the- Fractionconstructor. 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 - Fractionclass inherits from the abstract base class- numbers.Rational, and implements all of the methods and operations from that class.- Fractioninstances are hashable, and should be treated as immutable. In addition,- Fractionhas the following properties and methods:- Changed in version 3.2: The - Fractionconstructor now accepts- floatand- decimal.Decimalinstances.- Changed in version 3.9: The - math.gcd()function is now used to normalize the numerator and denominator.- math.gcd()always returns an- inttype. Previously, the GCD type depended on numerator and denominator.- Changed in version 3.11: Underscores are now permitted when creating a - Fractioninstance from a string, following PEP 515 rules.- Changed in version 3.11: - Fractionimplements- __int__now to satisfy- typing.SupportsIntinstance checks.- Changed in version 3.12: Space is allowed around the slash for string inputs: - Fraction('2 / 3').- Changed in version 3.12: - Fractioninstances now support float-style formatting, with presentation types- "e",- "E",- "f",- "F",- "g",- "G"and- "%"".- Changed in version 3.13: Formatting of - Fractioninstances without a presentation type now supports fill, alignment, sign handling, minimum width and grouping.- 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 - Trueif the Fraction is an integer.- Added in version 3.12. 
 - classmethod from_float(flt)¶
- Alternative constructor which only accepts instances of - floator- numbers.Integral. Beware that- Fraction.from_float(0.3)is not the same value as- Fraction(3, 10).
 - classmethod from_decimal(dec)¶
- Alternative constructor which only accepts instances of - decimal.Decimalor- numbers.Integral.- Note - From Python 3.2 onwards, you can also construct a - Fractioninstance directly from a- decimal.Decimalinstance.
 - limit_denominator(max_denominator=1000000)¶
- Finds and returns the closest - Fractionto- selfthat 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 the- math.floor()function:- >>> from math import floor >>> floor(Fraction(355, 113)) 3 
 - __ceil__()¶
- Returns the least - int- >= self. This method can also be accessed through the- math.ceil()function.
 - __round__()¶
- __round__(ndigits)
- The first version returns the nearest - intto- self, rounding half to even. The second version rounds- selfto the nearest multiple of- Fraction(1, 10**ndigits)(logically, if- ndigitsis negative), again rounding half toward even. This method can also be accessed through the- round()function.
 - __format__(format_spec, /)¶
- Provides support for formatting of - Fractioninstances via the- str.format()method, the- format()built-in function, or Formatted string literals.- If the - format_specformat 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_specformat specification string ends with one of the presentation types- 'e',- 'E',- 'f',- 'F',- 'g',- 'G'or- '%'then formatting follows the rules outlined for the- floattype 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.