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

The most reasonable value of n  n = -2.

We have given that the length of the football field = 300 feet

It can also be expressed as approximately  $5.7\times 10^{n}miles$

What is the value of one mile in feet?

Also, 1 mile = 5280 feet....(1)

We have to find 1 feet so divide both side of equation (1)by by 5280 we get,

$1feet=\frac{1}{5280}$

Now, for 300 feet is,

$300feet=\frac{1}{5280}(300)$

$300 feet=0.056818181=0.057miles$

In scientific notation we have,

$300 feet=5.7\times 10^{-2}miles$

Therefore we get  n = -2.

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