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The image contains a set of math problems asking to perform indicated operations and express the final answer with the correct number of significant figures. I'll analyze and solve each problem based on the visible information:

1. **Problem 1:**
   \[
   \frac{(6.998 \times 10^3) - (6.9 \times 10^3)}{2.50 \times 10^3}
   \]

   **Solution:**
   \[
   6.998 \times 10^3 = 6998
   \]
   \[
   6.9 \times 10^3 = 6900
   \]
   \[
   6998 - 6900 = 98
   \]
   \[
   \text{Then, } \frac{98}{2.50 \times 10^3} = \frac{98}{2500} = 0.0392
   \]

   The answer should have 3 significant figures (based on the given values):
   \[
   \boxed{3.92 \times 10^{-2}}
   \]

2. **Problem 2:**
   \[
   \sqrt{(7.835 \times 10^4) \times (4.98 \times 10^2)} 
   \]

   **Solution:**
   \[
   7.835 \times 10^4 = 78350
   \]
   \[
   4.98 \times 10^2 = 498
   \]
   \[
   78350 \times 498 = 3.9 \times 10^7
   \]
   \[
   \sqrt{3.9 \times 10^7} \approx 6248.992
   \]

   The answer should be rounded based on the least number of significant figures in the given numbers:
   \[
   \boxed{6.25 \times 10^3}
   \]

3. **Problem 3:**
   \[
   \sqrt{4.550^2 + 9.887^2 + 2.98^2}
   \]

   **Solution:**
   \[
   4.550^2 = 20.7025
   \]
   \[
   9.887^2 = 97.7681
   \]
   \[
   2.98^2 = 8.8804
   \]
   \[
   \text{Adding the squares: } 20.7025 + 97.7681 + 8.8804 = 127.351
   \]
   \[
   \sqrt{127.351} \approx 11.29
   \]

   The answer should reflect significant figures from the values involved:
   \[
   \boxed{11.3}
   \]

4. **Problem 4:**
   \[
   6.78 + 5.903 + 6.8 \times 10^2
   \]

   **Solution:**
   \[
   6.8 \times 10^2 = 680
   \]
   \[
   6.78 + 5.903 + 680 = 692.683
   \]

   Corrected to significant figures (least decimal places):
   \[
   \boxed{692.7}
   \]

5. **Problem 5:**
   \[
   \frac{5.876 \times 10^5}{4.520 \times 10^2}
   \]

   **Solution:**
   \[
   5.876 \times 10^5 = 587600
   \]
   \[
   4.520 \times 10^2 = 452.0
   \]
   \[
   \frac{587600}{452.0} \approx 1299.1
   \]

   Adjusting to significant figures:
   \[
   \boxed{1.299 \times 10^3}
   \]

Would you like more details on any of these solutions or have any questions?

Here are some related questions for practice:
1. What are the rules for determining significant figures in multiplication and division?
2. How do you handle significant figures when adding and subtracting?
3. What is the general process for calculating the square root of a large number by hand?
4. Why is it important to consider significant figures in scientific calculations?
5. How do logarithms affect the significant figures of a result?

**Tip:** When dealing with significant figures, always consider the number of decimal places in addition/subtraction and the total number of significant figures in multiplication/division.

Perform the indicated operation. Express your final answer to the correct number of significant figures.

Learn how to perform operations with significant figures in scientific notation and express final answers correctly. This detailed solution explains the rules for significant figures, square root calculations, and arithmetic operations. Suitable for students in Grades 10-12.

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