Floating point numbers

Decimals are usually stored as IEEE 754 floating point numbers: a sign, an exponent and a binary fraction, 64 bits in a double. Think of 1/3, which cannot be written exactly in decimal. In the same way, 0.1 cannot be written exactly in binary.

So 0.1 + 0.2 gives 0.30000000000000004, and 0.1 + 0.2 == 0.3 is false. The errors are tiny, but they add up in loops and break equality checks. Compare floats with a tolerance, a small allowed difference, such as abs(a - b) < 1e-9.

Never store money in a float. Use whole cents in an integer, or a decimal type such as Python's Decimal, Java's BigDecimal or C#'s decimal. This answers the first part of the milestone.