Question

A football field measures 300 feet in length. It can also be expressed as approximately 5.7x10ⁿ miles. If there are 5,280 feet in 1 mile, which is the most reasonable value of n?

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

Answer 1

To convert 300 feet to miles, divide by 5,280 to get 0.0568 miles, which is approximately 5.7x10⁻² when expressed in scientific notation. Thus, the most reasonable value for n is -2.

Step-by-step explanation:

The football field measures 300 feet in length. Given that there are 5,280 feet in 1 mile, we need to express 300 feet as a decimal fraction of a mile and then in the form of scientific notation, which is approximately 5.7x10ⁿ miles. To do this, divide 300 by 5,280 to get approximately 0.0568 miles. Now to express 0.0568 as scientific notation, we adjust the decimal place to obtain 5.68, which would translate to 5.68x10⁻² in scientific notation (since we moved the decimal point two places to the right, 'n' = -2).

To find the most reasonable value of n, we need to convert the length of the football field from feet to miles using the given conversion factor of 5,280 feet in 1 mile.

First, we divide 300 feet by 5,280 feet per mile:

300 feet ÷ 5,280 feet/mile = 0.056818182 miles

This can be expressed in scientific notation as approximately 5.7 x 10-2 miles. Therefore, the most reasonable value of n is -2.

Therefore, the most reasonable value for 'n' in the expression 5.7x10ⁿ miles is -2, which corresponds to the option B.) -2.