Question

The total number of digits used in numbering the pages of a book having 366 pages is:

• A. 980
• B. 990
• C. 950
• D. 1000

Hint:

To count the number of digits used in page numbers, break it into ranges based on the number of digits (1-digit, 2-digit, 3-digit, etc.).

Answer 1

The Correct Option is B

Step 1: Count the digits used for pages 1 to 9.
Each of these pages uses 1 digit, so for 9 pages, the total number of digits is: \[ 9 \times 1 = 9 \text{ digits}. \] Step 2: Count the digits used for pages 10 to 99.
Each of these pages uses 2 digits, and there are \( 99 - 10 + 1 = 90 \) pages in this range. Thus, the total number of digits is: \[ 90 \times 2 = 180 \text{ digits}. \] Step 3: Count the digits used for pages 100 to 366.
Each of these pages uses 3 digits, and there are \( 366 - 100 + 1 = 267 \) pages in this range. Thus, the total number of digits is: \[ 267 \times 3 = 801 \text{ digits}. \] Step 4: Total number of digits.
The total number of digits is: \[ 9 + 180 + 801 = 990 \text{ digits}. \]