To find out how many times the number 3 appears between 300 and 400, we can consider each place value separately. From 300 to 399, the number 3 appears 100 times as the hundreds digit. Additionally, the number 3 appears 100 times as the tens digit (from 30 to 39). So, in total, the number 3 appears 200 times between 300 and 400.