The number of times the digit 3 will be written when listing the integers from 1 to 1000, is

Options

A. 269
B. 271
C. 300
D. 302

Explanation

To find the number of times the digit '3' is written when listing the integers from 1 to 1000, we can break down the problem into three parts: counting occurrences of '3' in the units place, the tens place, and the hundreds place.

### Step-by-Step Solution:

1. **Count occurrences of '3' in the units place:**
- The numbers from 1 to 1000 can be grouped into sets of 10: (1-10, 11-20, ..., 991-1000).
- In each complete set of 10 numbers, the digit '3' appears once in the units place (e.g., 3, 13, 23, ..., 993).
- There are 100 complete sets of 10 in the range from 1 to 1000.
- Therefore, the number of times '3' appears in the units place is:
\[ 100 \text{ (sets)} \times 1 \text{ (occurrence per set)} = 100. \]

2. **Count occurrences of '3' in the tens place:**
- The numbers can also be grouped into sets of 100: (1-100, 101-200, ..., 901-1000).
- In each complete set of 100 numbers, the digit '3' appears in the tens place for the numbers 30 to 39.
- This gives us 10 occurrences of '3' in the tens place for each set of 100.
- There are 10 complete sets of 100 in the range from 1 to 1000.
- Therefore, the number of times '3' appears in the tens place is:
\[ 10 \text{ (sets)} \times 10 \text{ (occurrences per set)} = 100. \]

3. **Count occurrences of '3' in the hundreds place:**
- The hundreds place can only contain '3' for the numbers 300 to 399.
- This gives us 100 occurrences of '3' in the hundreds place.
- Therefore, the number of times '3' appears in the hundreds place is:
\[ 100. \]

4. **Total occurrences of '3':**
- Now, we add the occurrences from the units, tens, and hundreds places:
\[ \text{Total} = 100 \text{ (units)} + 100 \text{ (tens)} + 100 \text{ (hundreds)} = 300. \]

Thus, the digit '3' will be written **300 times** when listing the integers from 1 to 1000.