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 the intermediate calculation, we say there are "M−N" guard digits. Guard digits are also used in floating point operations in most computer systems. Given formula_1 we have to line up the binary points. This means we must add an extra digit to the first operand—a guard digit. This gives us formula_2. Performing this operation gives us formula_3 or formula_4. Without using a guard digit we have formula_5, yielding formula_6 or formula_7. This gives us a relative error of 1. Therefore, we can see how important guard digits can be. An example of the error caused by floating point roundoff is