Step-by-step Solution:

To determine how many times the digit 2 appears when listing all numbers from 1 to 1000, we can break it down into the following cases:
1. For the units place:
- In the units place, the digit 2 appears once every ten numbers (2, 12, 22, ..., 992). So, in the units place, the digit 2 appears 100 times (10 times for each hundred).
2. For the tens place:
- In the tens place, the digit 2 appears ten times in each hundred (20, 21, 22, ..., 29). So, in the tens place, the digit 2 appears 100 times (once in each hundred).
3. For the hundreds place:
- In the hundreds place, the digit 2 appears 100 times in the numbers 200 to 299.
Therefore, the digit 2 appears a total of 100 + 100 + 100 = 300 times when listing all numbers from 1 to 1000.