Question

the circumference of the earth is approximately 1.31 x 10^8 feet. if there are 5,280 feet in a mile, about how many miles is the circumference of the earth? a 2.48 x 10^12 miles b 2.48 x 10^4 miles c 2.48 x 10^-12 miles d 6.92 x 10^11 miles e 6.92 x 10^5 miles

Explanation:

Step1: Set up the conversion formula

To convert feet to miles, we divide the number of feet by the number of feet in a mile. So we have $\frac{1.31\times 10^{8}}{5280}$.

Step2: Rewrite 5280 in scientific - notation

$5280 = 5.28\times10^{3}$. Then the expression becomes $\frac{1.31\times 10^{8}}{5.28\times10^{3}}$.

Step3: Use the quotient - rule of exponents

The quotient - rule states that $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$. So $\frac{1.31}{5.28}\times10^{8 - 3}$.

Step4: Calculate the coefficient

$\frac{1.31}{5.28}\approx0.248$.

Step5: Combine the coefficient and the exponent

$0.248\times10^{5}$.

Step6: Rewrite in proper scientific - notation

$2.48\times 10^{4}$.

Answer:

B. $2.48\times 10^{4}$ miles