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.
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class fractions.Fraction(numerator=0, denominator=1)¶
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class fractions.Fraction(other_fraction)
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class fractions.Fraction(float)
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class fractions.Fraction(decimal)
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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. 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.- 
numerator¶
- Numerator of the Fraction in lowest term. 
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denominator¶
- Denominator of the Fraction in lowest term. 
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from_float(flt)¶
- This class method constructs a - Fractionrepresenting the exact value of flt, which must be a- float. Beware that- Fraction.from_float(0.3)is not the same value as- Fraction(3, 10).
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from_decimal(dec)¶
- This class method constructs a - Fractionrepresenting the exact value of dec, which must be a- decimal.Decimalinstance.- Note - From Python 3.2 onwards, you can also construct a - Fractioninstance directly from a- decimal.Decimalinstance.
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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) 
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__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 
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__ceil__()¶
- Returns the least - int- >= self. This method can also be accessed through the- math.ceil()function.
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__round__()¶
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__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.
 
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fractions.gcd(a, b)¶
- Return the greatest common divisor of the integers a and b. If either a or b is nonzero, then the absolute value of - gcd(a, b)is the largest integer that divides both a and b.- gcd(a,b)has the same sign as b if b is nonzero; otherwise it takes the sign of a.- gcd(0, 0)returns- 0.- Deprecated since version 3.5: Use - math.gcd()instead.
See also
- Module numbers
- The abstract base classes making up the numeric tower. 
