Final answer:
The expression (5.3 x 10⁻³)(8.06 x 10²) is calculated to be 42.718, but when rounded to three significant figures as required by the question, the answer is 42.7.
Step-by-step explanation:
The question requires using significant figures in calculations of various mathematical expressions to ensure precision as per scientific notations. For the expression (5.3 x 10⁻³)(8.06 x 10²), both numbers have three significant figures, hence the answer should also be reported with three significant figures.
Calculating the expression: (5.3 x 10⁻³)(8.06 x 10²) equals 42.718 when not rounded. However, considering significant figures, we must round this answer to three significant figures, resulting in 42.7.
The general rule for multiplication is that the final result should have the same number of significant figures as the number with the fewest significant figures in the problem.