The digit 9 occurs 20 times between 1 and 100.
Between 1 and 100, the digit 9 appears nine times between 1 and 89 i.e. 9, 19, 29, 39, 49, 59, 69, 79, and 89, and it appears 11 times between 90 and 99 i.e. 90, 91, 92, 93, 94, 95, 96, 97, 98, and 99, adding up to a total of 20 occurrences.
Numbers with the digit 9 in the units place occur every 10 numbers, starting from 9, 19, 29, …, 89. There are a total of 9 such intervals (1-9, 10-19, …, 80-89), each containing one occurrence of the digit 9. So, there are 9 occurrences of the digit 9 in the units place.
When considering the occurrences of the digit 9 in the tens place between 1 and 100, we have 10 occurrences in the number occurrences, and two additional occurrences in the number 99, resulting in a total of 11 occurrences.
Adding the occurrences from the units and tens places, we get a total of 9 + 11 = 20 occurrences of the digit 9 between 1 and 100.