Let's work through the problems one by one. The key here is to ensure that the final answers are expressed with the correct number of significant figures.

Problem 1

$(6.022 \times 10^3) \div (3.44 \times 10^2) = ?$

Solution: $\frac{6.022 \times 10^3}{3.44 \times 10^2} = \frac{6.022}{3.44} \times 10^{3-2} = 1.750581395 \times 10^1$ Since 6.022 has 4 significant figures and 3.44 has 3 significant figures, the final answer should have 3 significant figures: $\boxed{17.5}$

Problem 2

$3.00 \times 10^8 \times (4.00 \times 10^2 + 6.00 \times 10^3) = ?$

Solution: $3.00 \times 10^8 \times (4.00 \times 10^2 + 6.00 \times 10^3) = 3.00 \times 10^8 \times 6.40 \times 10^3 = 1.92 \times 10^{12}$ Here, since all numbers are to 3 significant figures, the final answer should also be to 3 significant figures: $\boxed{1.92 \times 10^{12}}$

Problem 3

$1902 \times 10^5 \div (5.008 \times 10^{-2}) = ?$

Solution: $\frac{1902 \times 10^5}{5.008 \times 10^{-2}} = \frac{1902}{5.008} \times 10^{5+2} = 379.7559842 \times 10^7 \approx 3.7976 \times 10^9$ The number 1902 has 4 significant figures, and 5.008 has 4 significant figures, so the final answer should have 4 significant figures: $\boxed{3.798 \times 10^9}$

Problem 4

$4.87 \times 10^{-5} - 4.60 \times 10^{-6} = ?$

Solution: $4.87 \times 10^{-5} - 4.60 \times 10^{-6} = (4.87 - 0.046) \times 10^{-5} = 4.824 \times 10^{-5}$ Since both numbers have 3 significant figures, the final answer should be: $\boxed{4.82 \times 10^{-5}}$

Problem 5

$7.432 \times 4.3 = ?$

Solution: $7.432 \times 4.3 = 31.9576$ Since 4.3 has 2 significant figures, the final answer should have 2 significant figures: $\boxed{32}$

Would you like any further details or explanations?

Here are five questions that extend this material:

1. How do you determine the correct number of significant figures in multiplication and division?
2. What rules do you apply for significant figures in addition and subtraction?
3. How do you handle significant figures when dealing with very small or very large numbers?
4. Why is it important to use the correct number of significant figures in scientific calculations?
5. Can you provide an example of a real-world scenario where significant figures are critical?

Tip: Always double-check the operations and significant figures, especially when combining multiple operations (like addition followed by multiplication).