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
Check digit a single check digit added to the original number, the system will not always capture "multiple" errors, such as two replacement errors (12 → 34) though, typically, double errors will be caught 90% of the time (both changes would need to change the output by offsetting amounts). A very simple check digit method would be to take the sum of all digits (digital sum) modulo 10. This would catch any single-digit error, as such an error would always change the sum, but does not catch any transposition errors (switching two digits) as re-ordering does not change the sum. A slightly