Question

What is the total number of digits required in numbering the pages of a book, which has 1,200 pages?

Answer 1

`\large\boxed{3,693}`

Explanation:

Break up the problem into smaller parts:

The total number of digits will be equal to the digits * the amount of numbers.

1 ⇒ 9 Digits each: 1 Amount of #s: 9 Total digits: 1(9) = 9

10 ⇒ 99 Digits each: 2 Amount of #s: 90 Total digits: 2(90) = 180

100 ⇒ 999 Digits each: 3 Amount of #s: 900 Total digits: 3(900) = 2,700

1000 ⇒ 1200 Digits each: 4 Amount of #s: 201 Total digits: 4(201) = 804

Add together all of the parts

9 + 180 + 2,700 + 804

`\large\boxed{3,693}`

Hope this helps :)