11.8. Decimal Floating Point Arithmetic

The decimal module offers a Decimal datatype for decimal floating point arithmetic. Compared to the built-infloat implementation of binary floating point, the class is especially helpful for

• financial applications and other uses which require exact decimal representation,
• control over precision,
• control over rounding to meet legal or regulatory requirements,
• tracking of significant decimal places, or
• applications where the user expects the results to match calculations done by hand.

For example, calculating a 5% tax on a 70 cent phone charge gives different results in decimal floating point and binary floating point. The difference becomes significant if the results are rounded to the nearest cent:

>>> from decimal import *
>>> x = Decimal('0.70') * Decimal('1.05')
>>> x
Decimal('0.7350')
>>> x.quantize(Decimal('0.01'))  # round to nearest cent
Decimal('0.74')
>>> round(.70 * 1.05, 2)         # same calculation with floats
0.73

The Decimal result keeps a trailing zero, automatically inferring four place significance from multiplicands with two place significance. Decimal reproduces mathematics as done by hand and avoids issues that can arise when binary floating point cannot exactly represent decimal quantities.

Exact representation enables the Decimal class to perform modulo calculations and equality tests that are unsuitable for binary floating point:

>>> Decimal('1.00') % Decimal('.10')
Decimal('0.00')
>>> 1.00 % 0.10
0.09999999999999995

>>> sum([Decimal('0.1')]*10) == Decimal('1.0')
True
>>> sum([0.1]*10) == 1.0
False

The decimal module provides arithmetic with as much precision as needed:

>>> getcontext().prec = 36
>>> Decimal(1) / Decimal(7)
Decimal('0.142857142857142857142857142857142857')