To count the 9s between 1 and 100: Count 9s in the units place (9, 19, 29, 39, 49, 59, 69, 79, 89, 90-99 excluded) = 10. Count 9s in the tens place (90, 91, 92, 93, 94, 95, 96, 97, 98, 99) = 10. Total = 20. Note: 99 contains two 9s and is counted in both groups.