Understanding Rounding Off
Rounding off is a mathematical technique used to simplify numbers for easier calculations. In this case, we will round off the numbers 5691 and 2120 to the nearest thousand before performing the addition.

Step 1: Rounding 5691
- When rounding 5691 to the nearest thousand:
- Identify the hundreds place (6 in this case).
- Since 6 is greater than or equal to 5, round up.
- Thus, 5691 rounds to **6000**.

Step 2: Rounding 2120
- When rounding 2120 to the nearest thousand:
- Identify the hundreds place (1 here).
- Since 1 is less than 5, round down.
- Therefore, 2120 rounds to **2000**.

Step 3: Adding the Rounded Numbers
- Now that we have the rounded values:
- 6000 (from 5691) + 2000 (from 2120)
- Performing the addition gives us:
- **6000 + 2000 = 8000**.

Conclusion
By rounding off the numbers to the nearest thousand and then adding them, we find that:
- The estimated sum of **5691 + 2120** is **8000**.
This method of rounding is especially useful in UPSC exams, where quick estimations can save valuable time during calculations.