The number of digits in a positive integer N is floor($log_{10}$(N)) + 1. The integer part of $log_{10}$(N) is called the characteristic. For N = 2^100: $log_{10}$(2^100) = 100*$log_{10}$(2) = 100*0.3010 = 30.10, so digits = 30 + 1 = 31. Similarly, the number of zeros after the decimal point in a small number like (0.5)^20 is given by the characteristic of its log.