Rounding

Summary

Rounding replaces a number by a nearby number from a fixed set, such as the integers, the numbers with two decimals, or the floating-point numbers. Rounding to nearest picks the closest element and needs a rule for ties, such as rounding half to even. Directed rounding always goes down, up or toward zero; the floor function is rounding down to an integer. In a computer every arithmetic result is rounded, and the difference is the round-off error.