Persistence of a number assumed. The single-digit final state reached in the process of calculating an integer's additive persistence is its digital root. Put another way, a number's additive persistence counts how many times we must sum its digits to arrive at its digital root. The additive persistence of 2718 is 2: first we find that 2 + 7 + 1 + 8 = 18, and then that 1 + 8 = 9. The multiplicative persistence of 39 is 3, because it takes three steps to reduce 39 to a single digit: 39 → 27 → 14 → 4. Also, 39 is the smallest
Guard digit Guard digit In numerical analysis, one or more guard digits can be used to reduce the amount of roundoff error. For example, suppose that the final result of a long, multi-step calculation can be safely rounded off to "N" decimal places. That is to say, the roundoff error introduced by this final roundoff makes a negligible contribution to the overall uncertainty. However, it is quite likely that it is "not" safe to round off the intermediate steps in the calculation to the same number of digits. Be aware that roundoff errors can accumulate. If "M" decimal places are used in