Question

apply your knowledge of operations with scientific notation to answer 7 - 8. 7. there are approximately 1.2 x 10^8 households in the u.s. if the average household uses 400 gallons of water each day, what is the total number of gallons of water used by households in the u.s. each day? 8. the population of china is about 1.4 x 10^9 people, while the population of south korea is approximately 50,000,000 people. how many times greater is the population of china than the population of south korea? scientific: _ standard: _ scientific: _ standard: _

Explanation:

Step1: Calculate total water - usage in the U.S.

Multiply number of households by water - usage per household. $400 = 4\times10^{2}$, number of households is $1.2\times 10^{8}$. So total water - usage is $(4\times 10^{2})\times(1.2\times 10^{8})$.
Using the rule of exponents $a^{m}\times a^{n}=a^{m + n}$ and $(ab)\times(cd)=(a\times c)\times(b\times d)$, we have $(4\times1.2)\times(10^{2}\times10^{8}) = 4.8\times10^{10}$. In standard form, $4.8\times10^{10}=48000000000$.

Step2: Calculate population ratio

Population of China is $1.4\times 10^{9}$, population of South - Korea is $50000000 = 5\times 10^{7}$.
To find how many times greater the population of China is than that of South - Korea, divide the population of China by the population of South - Korea: $\frac{1.4\times 10^{9}}{5\times 10^{7}}$.
Using the rule $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we get $\frac{1.4}{5}\times10^{9 - 7}=0.28\times10^{2}=2.8\times 10^{1}$. In standard form, $2.8\times 10^{1}=28$.

Answer:

1. Scientific: $4.8\times 10^{10}$, Standard: $48000000000$
2. Scientific: $2.8\times 10^{1}$, Standard: $28$