If you were to write out all the whole numbers from 1 to 1,000, how many...

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

Expert Solution

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.

orchestra answered 2 years ago

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