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Fractions and decimals

Let's finish the tour of the number department with a look at fractions and decimals. Fractions hold a rational numerator and denominator in their lowest forms. Let's see a quick example:

>>> from fractions import Fraction
>>> Fraction(10, 6)  # mad hatter?
Fraction(5, 3)  # notice it's been simplified
>>> Fraction(1, 3) + Fraction(2, 3)  # 1/3 + 2/3 == 3/3 == 1/1
Fraction(1, 1)
>>> f = Fraction(10, 6)
>>> f.numerator
5
>>> f.denominator
3

Although they can be very useful at times, it's not that common to spot them in commercial software. Much easier instead, is to see decimal numbers being used in all those contexts where precision is everything; for example, in scientific and financial calculations.

It's important to remember that arbitrary precision decimal numbers come at a price in performance, of course. The amount of data to be stored for each number is far greater than it is for fractions or floats as well as the way they are handled, which causes the Python interpreter much more work behind the scenes. Another interesting thing to note is that you can get and set the precision by accessing decimal.getcontext().prec.

Let's see a quick example with decimal numbers:

>>> from decimal import Decimal as D  # rename for brevity
>>> D(3.14)  # pi, from float, so approximation issues
Decimal('3.140000000000000124344978758017532527446746826171875')
>>> D('3.14')  # pi, from a string, so no approximation issues
Decimal('3.14')
>>> D(0.1) * D(3) - D(0.3)  # from float, we still have the issue
Decimal('2.775557561565156540423631668E-17')
>>> D('0.1') * D(3) - D('0.3')  # from string, all perfect
Decimal('0.0')
>>> D('1.4').as_integer_ratio()  # 7/5 = 1.4 (isn't this cool?!)
(7, 5)

Notice that when we construct a Decimal number from a float, it takes on all the approximation issues float may come from. On the other hand, when the Decimal has no approximation issues (for example, when we feed an int or a string representation to the constructor), then the calculation has no quirky behavior. When it comes to money, use decimals.

This concludes our introduction to built-in numeric types. Let's now look at sequences.

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