Question
There are 179 pages in a book.How many digits in all are used to print the page numbers?
Answers
GPT-4o mini
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**.
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**.