Question

a suns mass is approximately 2 x 10^30 kg. the earths mass is approximately 6 x 10^24 kg. about how many times more massive is the sun than the earth?
a. 2 x 10^6
b. 3.3 x 10^5
c. 33 x 10^6
d. 3 x 10^5
simplify.
a. 4 x 10^16
b. 4 x 10^ - 12
c. 8 x 10^8
d. 16 x 10^7

Explanation:

Step1: Set up the ratio

To find out how many times more massive the sun is than the Earth, we divide the mass of the sun by the mass of the Earth. Let $m_s = 2\times10^{30}$ kg (mass of the sun) and $m_e=6\times 10^{24}$ kg (mass of the Earth). The ratio is $\frac{m_s}{m_e}=\frac{2\times 10^{30}}{6\times 10^{24}}$.

Step2: Use exponent - division rule

According to the rule $\frac{a^m}{a^n}=a^{m - n}$ and $\frac{a}{b}\times\frac{10^m}{10^n}=\frac{a}{b}\times10^{m - n}$, we have $\frac{2\times 10^{30}}{6\times 10^{24}}=\frac{2}{6}\times10^{30 - 24}$.

Step3: Simplify the fraction and exponent

$\frac{2}{6}=\frac{1}{3}\approx0.33$, and $10^{30 - 24}=10^6$. So $\frac{1}{3}\times10^6 = 0.33\times10^6=3.3\times 10^5$.

Answer:

B. $3.3\times 10^5$