To solve the problem, we need to find the difference between the place values of the digit 8 in the greatest and smallest 4-digit numbers that can be formed using the digits 3, 8, 0, and 5.
### Step-by-Step Solution:
1. **Identify the digits**: The digits we have are 3, 8, 0, and 5.
2. **Form the greatest 4-digit number**:
- To form the greatest number, we arrange the digits in descending order.
- The largest digit is 8, followed by 5, then 3, and finally 0.
- Therefore, the greatest 4-digit number is **8530**.
3. **Form the smallest 4-digit number**:
- To form the smallest number, we need to ensure that the first digit is not 0 (as it would not be a 4-digit number).
- The smallest non-zero digit is 3, so we place 3 first.
- The remaining digits in ascending order after 3 are 0, 5, and 8.
- Therefore, the smallest 4-digit number is **3058**.
4. **Determine the place value of 8 in both numbers**:
- In **8530**, the place value of 8 is in the thousands place:
- Place value of 8 = 8 × 1000 = **8000**.
- In **3058**, the place value of 8 is in the units place:
- Place value of 8 = 8 × 1 = **8**.
5. **Calculate the difference between the place values**:
- Difference = Place value of 8 in greatest number - Place value of 8 in smallest number
- Difference = 8000 - 8 = **7992**.
### Final Answer:
The difference between the place values of 8 in the greatest and smallest 4-digit numbers formed by using the digits 3, 8, 0, and 5 is **7992**.
