What is the round-to-even rule?

Answer 1

The rounding rule which is usually taught in schools is that if the next digit is 1, 2, 3 or 4 then you round down while if it is 5, 6, 7, 8 or 9 then you round up - 0 is not rounded, of course. This means that if the "next" digit is random, then you round down less often than up: this introduces a upward bias in the result. The solution is to round 5 up half the time and down half the time. It would be possible to do this randomly but then the rounding is not reproducible: someone doing the same sum as you could round numbers differently and so come to a different answer.

The IEEE (Institute of Electronic and Electrical Engineers) standard 754 is to round 5 up or down so that the new last digit is even. This is the round to even rule.