There are:999 - 100 + 1 =900 3-digit numbers between 100 and 999
There are 271 numbers between 1 and 999 that have a 3 in them.
There are 19 numbers between 1 and 99 that have at least one 3 in them.
So: 271 - 19 =252 numbers between 100 and 999 that have at least one 3 in them.
900 - 252 = 648 numbers between 100 and 999 that have NO 3 in them.