Number of times the digit 5 will be written while listing the integers from 1 to 1000

For example if we want ti know for 1-100 we can also consider it as 0-99We already know 5 comes one time in 0-9 (1time) and this happens for 10 times for leading digit Uf we take number 0-99 (10times) and again 10 times for 50-59 [50,51,52.....59]Therefore it give us a total of (1)(10)+10=20timesSimilarily for 1-1000 or 0-99920 times for 0-99 and 10 times for 0-999Therefore (20)(10)=200And 100 times for 500-599 (100times)Therefore it give us a total of 200+100=300