If the question is "what is $645.02 rounded to the nearest dollar?" then:
We're rounding to the ones place. There's a 5 in the ones place. The next digit to the right (0) is less than 5, so the 5 in the ones place doesn't round up.
Answer: $645
.
If we wanted to be super-exact about it, 645.02 rounded to the nearest dollar is $0 because 645.02 is not a measure of money. For example, $5 is five dollars, but 5 is not five dollars (it's just 5). Your teacher is probably looking for the $645 version above though.