The problem asks to count how many times the digit 3 appears when counting from 1 to 100.
The digit 3 can appear in two positions: the units place and the tens place.
Numbers with 3 in the units place:
3, 13, 23, 33, 43, 53, 63, 73, 83, 93
This gives 10 occurrences.
Numbers with 3 in the tens place:
30, 31, 32, 33, 34, 35, 36, 37, 38, 39
This gives 10 occurrences.
Total occurrences =10+10
=20
Note that 33 contains two 3s (one in the units place and one in the tens place), and both are counted separately.
Therefore, the digit 3 appears 20 times when counting from 1 to 100.