Question

A football field measures 300 feet in length. It can also be expressed as approximately 5.7 times 10 Superscript n miles. If there are 5,280 feet in 1 mile, which is the most reasonable value of n?
Negative 3
Negative 2
2
3

Answer 1

To convert the length of the football field from feet to miles, we use the conversion factor that there are 5,280 feet in 1 mile.

Given that the football field measures 300 feet, we can set up the calculation as follows:

\[
\text{Length in miles} = \frac{300 \text{ feet}}{5,280 \text{ feet/mile}}
\]

Calculating this gives:

\[
\text{Length in miles} = \frac{300}{5,280} \approx 0.05682 \text{ miles}
\]

Now, we want to express this length in scientific notation as \( 5.7 \times 10^n \) miles.

To find \( n \), we need to express \( 0.05682 \) in that form.

We can rewrite \( 0.05682 \) as:

\[
0.05682 = 5.682 \times 10^{-2}
\]

Here, we have shifted the decimal two places to the right, which corresponds to \( 10^{-2} \).

Thus, \( 5.682 \) is approximately \( 5.7 \) when rounded, so we can say:

\[
0.05682 \approx 5.7 \times 10^{-2}
\]

With this, we identify that \( n \) is \(-2\).

Therefore, the most reasonable value of \( n \) is:

\[
\boxed{-2}
\]