Python - Numeric accuracy in fractions and decimals

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Introduction

Consider the following code

Demo

a = 1 / 3.0                     
b = 4 / 6.0                     #   ww w.j  ava 2s  .c o m
print( a )
print( b )
print( a + b )
print( a - b )
print( a * b )

Result

The value here is only as accurate as floating-point hardware Can lose precision over many calculations.

Both Fraction and Decimal provide ways to get exact results.

In the following example floating-point numbers do not accurately give the zero answer expected.

Demo

from fractions import Fraction 
from decimal import Decimal 
print( 0.1 + 0.1 + 0.1 - 0.3 )           # This should be zero (close, but not exact) 
print( Fraction(1, 10) + Fraction(1, 10) + Fraction(1, 10) - Fraction(3, 10) )
print( Decimal('0.1') + Decimal('0.1') + Decimal('0.1') - Decimal('0.3') )

Result

Fractions and decimals both have more intuitive and accurate results than floating points:

Demo

from fractions import Fraction 
from decimal import Decimal 
import decimal # ww w  .j  a v a  2 s  . c o  m
decimal.getcontext().prec = 2 
print( 1 / 3 )                           # Use a ".0" in Python 2.X for true "/" 
print( Fraction(1, 3) )                  # Numeric accuracy, two ways 
print( Decimal(1) / Decimal(3) )
print( (1 / 3) + (6 / 12) )              # Use a ".0" in Python 2.X for true "/" 
print( Fraction(6, 12) )                 # Automatically simplified 
print( Fraction(1, 3) + Fraction(6, 12) )
print( decimal.Decimal(str(1/3)) + decimal.Decimal(str(6/12)) )
print( 1000.0 / 1234567890 )
print( Fraction(1000, 1234567890) )      # Substantially simpler!

Result

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