Question

question 1-10
the earths surface area is approximately 200,000,000 square miles, and each square mile has an average population of 3.9 × 10^1
based on the information above, what is the total population of the earth expressed in scientific notation?
5.9 × 10^9
5.9 × 10^10
7.8 × 10^9
7.8 × 10^10

Explanation:

Step1: Write Earth's surface - area in scientific notation

The Earth's surface area is $200000000 = 2\times10^{8}$ square - miles.

Step2: Multiply surface area by population per square mile

The population per square mile is $3.9\times 10^{1}$. The total population $P$ is the product of the surface area $A$ and the population per square mile $p$, so $P=A\times p=(2\times 10^{8})\times(3.9\times 10^{1})$.

Step3: Use the rule of exponents for multiplication

According to the rule $a^{m}\times a^{n}=a^{m + n}$ and $(a\times b)\times(c\times d)=(a\times c)\times(b\times d)$, we have $(2\times 10^{8})\times(3.9\times 10^{1})=(2\times3.9)\times(10^{8}\times 10^{1}) = 7.8\times10^{8 + 1}=7.8\times 10^{9}$.

Answer:

C. $7.8\times 10^{9}$