Question

a football field measures 300 feet in length. it can also be expressed as approximately \\(5.7 \times 10^n\\) miles. if there are 5,280 feet in 1 mile, which is the most reasonable value of \\(n\\)?

-3
-2
2
3

Explanation:

Convert feet to miles

$$ \text{Length in miles} = \frac{300\text{ feet}}{5280\text{ feet/mile}} \approx 0.056818\text{ miles} $$

Express in scientific notation

$$ 0.056818 \approx 5.7 \times 10^{-2} $$

Determine the value of \(n\)

$$ 5.7 \times 10^n = 5.7 \times 10^{-2} \implies n = -2 $$

Answer:

• -3
• -2 (Correct answer)
• 2
• 3