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To find the total number of digits used in numbering the pages of a book with 552 pages, we can break this down into different categories based on the number of digits in the page numbers:

1. **Pages 1 to 9**: These are single-digit numbers. There are 9 pages, each using 1 digit.
   \[ 9 \text{ pages} \times 1 \text{ digit/page} = 9 \text{ digits} \]

2. **Pages 10 to 99**: These are double-digit numbers. There are \(99 - 10 + 1 = 90\) pages, each using 2 digits.
   \[ 90 \text{ pages} \times 2 \text{ digits/page} = 180 \text{ digits} \]

3. **Pages 100 to 552**: These are triple-digit numbers. There are \(552 - 100 + 1 = 453\) pages, each using 3 digits.
   \[ 453 \text{ pages} \times 3 \text{ digits/page} = 1359 \text{ digits} \]

Adding all these together gives the total number of digits used:

\[ 9 + 180 + 1359 = 1548 \text{ digits} \]

Thus, a total of 1548 digits are used in numbering the pages of the book. 

Would you like any further details or explanations on this topic? Here are some related questions you might consider:

1. How would the answer change if the book had 1000 pages?
2. How many digits would be used if the book started numbering from a page other than 1?
3. What pattern emerges in the number of digits used as the number of pages increases in a book?
4. Can you explain how this type of problem can be generalized for any number of pages?
5. What is the general formula for calculating the number of digits used in numbering pages up to any given number?

Tip: When approaching problems about page numbering, consider the ranges of digit lengths separately for a clearer calculation process.

Find the total number of digits used in numbering the pages of the book having 552 pages?

Learn how to find the total number of digits used in numbering a book with 552 pages. This problem involves breaking down page numbers into ranges and calculating the total digits used. Suitable for students in Grades 6-8.

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