============================= fractions -- Rational Numbers ============================= .. module:: fractions :synopsis: Implements a class for working with rational numbers. :Purpose: Implements a class for working with rational numbers. :Available In: 2.6 and later The Fraction class implements numerical operations for rational numbers based on the API defined by :class:`Rational` in :mod:`numbers`. Creating Fraction Instances =========================== As with :mod:`decimal`, new values can be created in several ways. One easy way is to create them from separate numerator and denominator values: .. include:: fractions_create_integers.py :literal: :start-after: #end_pymotw_header The lowest common denominator is maintained as new values are computed. .. {{{cog .. cog.out(run_script(cog.inFile, 'fractions_create_integers.py')) .. }}} :: \$ python fractions_create_integers.py 1/2 = 1/2 2/4 = 1/2 3/6 = 1/2 .. {{{end}}} Another way to create a Fraction is using a string representation of `` / ``: .. include:: fractions_create_strings.py :literal: :start-after: #end_pymotw_header .. {{{cog .. cog.out(run_script(cog.inFile, 'fractions_create_strings.py')) .. }}} :: \$ python fractions_create_strings.py 1/2 = 1/2 2/4 = 1/2 3/6 = 1/2 .. {{{end}}} Strings can also use the more usual decimal or floating point notation of ``[].[]``. .. include:: fractions_create_strings_floats.py :literal: :start-after: #end_pymotw_header .. {{{cog .. cog.out(run_script(cog.inFile, 'fractions_create_strings_floats.py')) .. }}} :: \$ python fractions_create_strings_floats.py 0.5 = 1/2 1.5 = 3/2 2.0 = 2 .. {{{end}}} There are class methods for creating Fraction instances directly from other representations of rational values such as float or :mod:`decimal`. .. include:: fractions_from_float.py :literal: :start-after: #end_pymotw_header Notice that for floating point values that cannot be expressed exactly the rational representation may yield unexpected results. .. {{{cog .. cog.out(run_script(cog.inFile, 'fractions_from_float.py')) .. }}} :: \$ python fractions_from_float.py 0.1 = 3602879701896397/36028797018963968 0.5 = 1/2 1.5 = 3/2 2.0 = 2 .. {{{end}}} Using :mod:`decimal` representations of the values gives the expected results. .. include:: fractions_from_decimal.py :literal: :start-after: #end_pymotw_header .. {{{cog .. cog.out(run_script(cog.inFile, 'fractions_from_decimal.py')) .. }}} :: \$ python fractions_from_decimal.py 0.1 = 1/10 0.5 = 1/2 1.5 = 3/2 2.0 = 2 .. {{{end}}} Arithmetic ========== Once the fractions are instantiated, they can be used in mathematical expressions as you would expect. .. include:: fractions_arithmetic.py :literal: :start-after: #end_pymotw_header .. {{{cog .. cog.out(run_script(cog.inFile, 'fractions_arithmetic.py')) .. }}} :: \$ python fractions_arithmetic.py 1/2 + 3/4 = 5/4 1/2 - 3/4 = -1/4 1/2 * 3/4 = 3/8 1/2 / 3/4 = 2/3 .. {{{end}}} Approximating Values ==================== A useful feature of Fraction is the ability to convert a floating point number to an approximate rational value by limiting the size of the denominator. .. include:: fractions_limit_denominator.py :literal: :start-after: #end_pymotw_header .. {{{cog .. cog.out(run_script(cog.inFile, 'fractions_limit_denominator.py')) .. }}} :: \$ python fractions_limit_denominator.py PI = 3.14159265359 No limit = 314159265359/100000000000 1 = 3 6 = 19/6 11 = 22/7 16 = 22/7 21 = 22/7 26 = 22/7 31 = 22/7 36 = 22/7 41 = 22/7 46 = 22/7 51 = 22/7 56 = 22/7 61 = 179/57 66 = 201/64 71 = 223/71 76 = 223/71 81 = 245/78 86 = 267/85 91 = 267/85 96 = 289/92 .. {{{end}}} .. seealso:: `fractions `_ The standard library documentation for this module. :mod:`decimal` The decimal module provides an API for fixed and floating point math. :mod:`numbers` Numeric abstract base classes.