Fixed-point and Floating-point Numbers

Definition

Floating-point numbers store values in binary with limited precision, so many decimal fractions such as 0.1 cannot be represented exactly. Fixed-point or decimal types store an amount as a whole number of a small unit, such as cents, which keeps addition and comparison of money exact.

In plain terms

Computers usually store non-integers as binary fractions. Just as one third cannot be written exactly in decimal, one tenth cannot be written exactly in binary, so each stored value is a very close neighbour. For measurements such as temperatures that is fine. For money, or for anything that must match to the last digit, the tiny errors add up and break equality checks.

The usual fix is to store the amount as an integer count of the smallest unit (cents) together with the currency, and to do arithmetic on integers. Rounding then happens in one place, by a rule you chose.

Example

In ordinary double-precision floating point:

The same sums in whole cents:

Common misunderstandings

• “Floating point is inaccurate, so never use it.” It is the right tool for measurements and scientific values; the problem is using it where exact decimal amounts are required.
• “Rounding at the end fixes it.” Sometimes, but errors can already have flipped a comparison or a total along the way.
• “Decimal types are too slow.” For the volumes of most business data the cost is negligible compared with a wrong total.