Question

A football field measures 300 feet in length. It can also be expressed as approximately

5.7 x 10^n .

If there are 5,280 feet in 1 mile , which is the most reasonable value of n.

Answer 1

Answer: n=-2

Step-by-step explanation:

Given

The length of the football field is  $300\ ft$

In the mile, it can be expressed as $5.7\times 10^n\ mile$

Also, $5280\ ft=1\ mile$ or

$1\ ft=\dfrac{1}{5280}\ miles\\\\1\ ft=1.893\times 10^{-4}\ miles$

converting $300\ ft$ to miles

$\Rightarrow 300\times 1.893\times 10^{-4}\\\Rightarrow 5.68\times 10^{-2}\approx 5.7\times 10^{-2}$

Comparing it with the given value $5.7\times 10^n\ mile$

we get $n=-2$