On the standard rounding rule for addition and subtraction

An investigation of the commonly suggested rounding rule for addition and s ubtraction is presented including its derivation from a basic assumption. T hrough theoretical study and Monte-Carlo simulations, it is shown that this rule predicts the minimum number of significant digits needed to preserve precision 100% of the time. Because the standard rounding rule for these tw o fundamental operations is accurate and completely safe for data, there is no need to extend this rule to keeping an additional significant figure as has suggested for multiplication and division.