Rounding Error

Basically this is half of the plot for the movie Office Space. If you haven’t seen it, go watch it. When we round any calculated value off to a specific number of digits, we’re creating an estimate of the actual value for the sake of simplicity or ease of use. That newly-rounded number has a slightly different value than the exact, actual value.

The difference between the rounded value and the actual value is the rounding error. If we calculated a value as 3.2518 and rounded it to the tenths place, i.e. 3.3, we’d have a rounding error of 3.3 – 3.2518 = 0.0482. It typically doesn’t matter what order we subtract in as we usually refer to the error by its absolute value which strips any negative signs off.