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A book starts on page 1 and is numbered on every page. If the total number of digits used is 516, how many pages are there in the book?

Respuesta :

Answer:

208

Step-by-step explanation:

First 9 pages 1-9    = 9 digits

pages 10 - 99 = 90 pages x 2 digits each = 180 digits

    total so far = 189 digits leaving   516 - 189 = 327 digits to be used

        every page from here until 999 requires 3 digits

                  327 / 3 = 109 more pages

109 + 90 + 9 = 208 pages in book

semsee45

Answer:

298

Step-by-step explanation:

The first 9 pages are numbered with single digit numbers:

  • 1, 2, 3, 4, 5, 6, 7, 8 and 9

Therefore, 9 digits are used to number the first 9 pages.

The next 90 pages are numbered with double-digit numbers:

  • 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
  • 20, 21, 22, 23, 24, 25, 26, 27, 28, 29

                                    . . .

  • 90, 91, 92, 93, 94, 95, 96, 97, 98, 99

Therefore, the pages numbered 10 to 99 use a total of 90 × 2 = 180 digits.

So far we have used 9 + 180 = 189 digits for pages 1 - 99 of the book.

Subtract 189 from the total number of digits used:

  • 516 - 189 = 327

The pages after page 99 are numbered with triple-digit numbers.

Divide the total remaining digits 327 by 3 to calculate the number of pages numbered with triple-digit numbers:

  • 327 ÷ 3 = 109

Therefore, the total number of pages in the book is:

  • 9 + 180 + 109 = 298

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