Roundoff errors.



In [1]:

    
a = .1



In [2]:

    
3 * a - .3









    Out[2]:





5.551115123125783e-17

Decimals also have rounding errors, and we understand them better.



In [3]:

    
from decimal import Decimal, getcontext



In [4]:

    
getcontext().prec = 2



In [5]:

    
a = Decimal('.1')
a









    Out[5]:





Decimal('0.1')



In [6]:

    
3 * a - Decimal('.3')









    Out[6]:





Decimal('0.0')

Fractions are pure and exact.



In [7]:

    
from fractions import Fraction



In [8]:

    
f = Fraction(3, 12)
f









    Out[8]:





Fraction(1, 4)



In [9]:

    
Fraction(1, 4) + Fraction(1, 3)









    Out[9]:





Fraction(7, 12)



In [10]:

    
Fraction(1, 4) + Fraction(1, 3) + Fraction(5, 12)









    Out[10]:





Fraction(1, 1)