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

Explanation:

Given

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

In the mile, it can be expressed as
`5.7* 10^n\ mile`

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

`1\ ft=(1)/(5280)\ miles\\\\1\ ft=1.893* 10^(-4)\ miles`

converting
`300\ ft` to miles

`\Rightarrow 300* 1.893* 10^(-4)\\\Rightarrow 5.68* 10^(-2)\approx 5.7* 10^(-2)`

Comparing it with the given value
`5.7* 10^n\ mile`

we get
`n=-2`