How many times do you have to write the digit '3', while writing numbers from 1 to 1000?

To find out how many times you have to write the digit '3' while writing numbers from 1 to 1000, you can break down the problem into smaller parts.

1. Count the number of times '3' appears in each place (units, tens, hundreds, thousands).

2. For the units place: There are 10 possible numbers for each of the tens, hundreds, and thousands places (0-9). So, for every 10 numbers, '3' will appear once in the units place. Therefore, in 1000 numbers, '3' will appear 1000/10 = 100 times in the units place.

3. For the tens place: Similar to the units place, for every 10 numbers, '3' will appear once in the tens place. Therefore, in 1000 numbers, '3' will appear 1000/10 = 100 times in the tens place.

4. For the hundreds place: For every 100 numbers, '3' will appear 10 times in the hundreds place (300-399). Therefore, in 1000 numbers, '3' will appear 10*10 = 100 times in the hundreds place.

5. For the thousands place: '3' appears once in the thousands place (in the number 3000), but since we're only counting up to 1000, '3' doesn't appear in the thousands place.

6. Add up the number of times '3' appears in each place: 100 (units) + 100 (tens) + 100 (hundreds) = 300.

So, you have to write the digit '3' 300 times while writing numbers from 1 to 1000.