Question

If you were to write out all the whole numbers from 1 to 1,000, how many zeroes would you have written?

Answer 1

The digit zero appears only in the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. Thus, there are 11 zeros among the digits from 1 to 99. This is the same as the number of digits in writing the numbers from 1 to 10

.Now let us look at the numbers from 1 to 1000. To write all these numbers down, we need to use 9+ 2(90) +3)900) +4 = 9 +180 + 2700 + 4 = 2893 digits to accommodate the 9 single-digit numbers, the 90 double-digit numbers, the 900 triple-digit numbers and the number 1000.

There are 9 numbers of the form a0. 9 numbers of the form a00 (each with two zeros), 81 numbers of the form a0k, 81 numbers of the form ak0, where a and k are one of the nine positive digits, and the number 1000.

So, answer=9 + 18 + 81 + 81 + 3 = 192.