Find the number of digits required to write down the number of pages in a 300 pages book.

Options

A. 792
B. 279
C. 729
D. none of these

Answer

To find the number of digits required to write down the page numbers in a 300-page book, we can break the problem down into three parts: the single-digit page numbers, the two-digit page numbers, and the three-digit page numbers.

### Step-by-Step Solution:

1. **Identify the ranges of page numbers:**
- Single-digit pages: 1 to 9
- Two-digit pages: 10 to 99
- Three-digit pages: 100 to 300

2. **Count the digits for single-digit pages (1 to 9):**
- There are 9 single-digit pages (1, 2, 3, 4, 5, 6, 7, 8, 9).
- Each of these pages has 1 digit.
- Total digits from single-digit pages = 9 pages × 1 digit = **9 digits**.

3. **Count the digits for two-digit pages (10 to 99):**
- There are 90 two-digit pages (from 10 to 99).
- Each of these pages has 2 digits.
- Total digits from two-digit pages = 90 pages × 2 digits = **180 digits**.

4. **Count the digits for three-digit pages (100 to 300):**
- There are 201 three-digit pages (from 100 to 300).
- Each of these pages has 3 digits.
- Total digits from three-digit pages = 201 pages × 3 digits = **603 digits**.

5. **Add all the digits together:**
- Total digits = Digits from single-digit pages + Digits from two-digit pages + Digits from three-digit pages
- Total digits = 9 + 180 + 603 = **792 digits**.

### Final Answer:
The total number of digits required to write down the page numbers in a 300-page book is **792**.

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