# Python - Numeric accuracy in fractions and decimals

## Introduction

Consider the following code

## Demo

```a = 1 / 3.0
b = 4 / 6.0                     # w  w w . ja  va  2  s.  c om
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 # from www.  j  a  v a2 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!

```