There are 179 pages in a book.How many digits in all are used to print the page numbers?

1 answer

To find out how many digits are used to print the page numbers from 1 to 179, we can break it down into segments based on the number of digits in the page numbers.

  1. Pages 1 to 9:

    • There are 9 pages.
    • Each page number has 1 digit.
    • Total digits used = \(9 \times 1 = 9\).
  2. Pages 10 to 99:

    • There are \(99 - 10 + 1 = 90\) pages.
    • Each page number has 2 digits.
    • Total digits used = \(90 \times 2 = 180\).
  3. Pages 100 to 179:

    • There are \(179 - 100 + 1 = 80\) pages.
    • Each page number has 3 digits.
    • Total digits used = \(80 \times 3 = 240\).

Now, we can sum all of these:

\[ 9 \text{ (for pages 1 to 9)} + 180 \text{ (for pages 10 to 99)} + 240 \text{ (for pages 100 to 179)} = 429 \]

Thus, the total number of digits used to print the page numbers from 1 to 179 is 429.