Question

A football field measures 300 feet in length. It can also be expressed as approximately 5.7x10^n miles. If there are 5,280 feet in 1 mile, which is the most reasonable value of n?

A.) -3. B.) -2. C.) 2 (incorrect.) D.) 3.

Answer 1

Answer: B.) -2.

Explanation:

Given: The length of the football field = 300 feet

It can also be expressed as approximately
`5.7*10^n\ miles.`

Also, 1 mile = 5280 feet

Therefore, 1 feet=
`(1)/(5280)\ mile`

Now, 300 feet=
`(1)/(5280)*300\ mile`

⇒ 300 feet=
`=0.0568181818182\approx0.057\ mile`

In scientific notation, 300 feet=
`5.7*10^(-2)`

When we compare to
`5.7*10^n\ miles.`

We get n = -2.

Answer 2

The answer is letter B) -2. To solve for this, you first have to divide 300 by the number of feet in 1 mile. It will be 300/5280 which will result to 0.05681818182. Then round off the value to 0.057 and express it in exponential term. Hope this helps.