How many digits are required to number a book containing 366 pages?

Options

A. 732
B. 990
C. 1098
D. 1305

Explanation

To find out how many digits are required to number a book containing 366 pages, we can break it down into segments based on the number of digits in the page numbers.

### Step 1: Count the pages from 1 to 9
- The pages from 1 to 9 are single-digit numbers.
- There are 9 pages in total (1, 2, 3, 4, 5, 6, 7, 8, 9).
- Each of these pages requires 1 digit.

**Calculation:**
- Total digits for pages 1 to 9 = 9 pages × 1 digit = 9 digits.

### Step 2: Count the pages from 10 to 99
- The pages from 10 to 99 are two-digit numbers.
- The total number of pages in this range can be calculated as follows:
- Total pages = 99 - 10 + 1 = 90 pages (from 10 to 99 inclusive).
- Each of these pages requires 2 digits.

**Calculation:**
- Total digits for pages 10 to 99 = 90 pages × 2 digits = 180 digits.

### Step 3: Count the pages from 100 to 366
- The pages from 100 to 366 are three-digit numbers.
- The total number of pages in this range can be calculated as follows:
- Total pages = 366 - 100 + 1 = 267 pages (from 100 to 366 inclusive).
- Each of these pages requires 3 digits.

**Calculation:**
- Total digits for pages 100 to 366 = 267 pages × 3 digits = 801 digits.

### Step 4: Add all the digits together
Now, we will sum up the total digits calculated from each range:

**Total Digits:**
- From pages 1 to 9: 9 digits
- From pages 10 to 99: 180 digits
- From pages 100 to 366: 801 digits

**Final Calculation:**
Total digits = 9 + 180 + 801 = 990 digits.

### Conclusion:
The total number of digits required to number a book containing 366 pages is **990**.

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