This kind of thing comes up in deciding how to round floats as well. If you always round up or round down, the errors accumulate linearly. Floats use round-to-

This kind of thing comes up in deciding how to round floats as well. If you always round up or round down, the errors accumulate linearly. Floats use round-to-even [1] to prevent this, although even that method accumulates error proportional to sqrt(number of ops). [1] https://en.wikipedia.org/wiki/Rounding#Round_half_to_even https://en.wikipedia.org/wiki/Rounding#Round_half_to_even