I got a math test and this is one of the questions. How many 3 are in between 100-600 and how many 7 are in between 100-600

Since 600 has no 3's we will ignore it, so we are only going to be dealing with 100 to 599. First thing is to figure out how many 3's are between 0 and 9. Easy enough there is just one. Now how many 3's are between 0 and 99? Well there is one for every multiple of ten, that is between 20 and 29 there is one, between 70 and 79 there is one, and so on. So that makes ten 3's in the one's place between 0 and 99. So far we have ten 3's, but there is also the ten's place, that is there are also ten additional 3's for 30, 31, 32, etc. so there are twenty 3's between 0 and 99. Well there are also twenty 3's between 100 and 199, and for every block of a hundred between 100 and 599 except for the block of numbers between 300 and 399, these have an additional hundred 3's because of 300, 301, 302, etc. There are five blocks of a hundred between 100 and 600, to see this look at it like this 100-199, 200-299, 300-399, 400-499, 500-599. So we have 20 + 20 + 20 + 20 +20 which gives us one hundred, plus the additional hundred for 300 -399, which brings our grand total to two-hundred 3's between 100 and 600.

The question with the 7's is solved identically, except you don't have to deal with the 700-799 block.

I hope this helps :)