Question

earth has an estimated mass of 5,972,000,000,000,000,000,000 kg. choose the best approximation of the earths mass. choose 1 answer: a 6·10²¹ kg b 6·10²⁴ kg approximately how many times as large is the earths mass as liams mass? choose 1 answer: a 6·10²⁰ b 6·10²¹ c 6·10²²

Explanation:

Step1: Identify Earth's mass approximation

The Earth's mass is approximately $5,972,000,000,000,000,000,000,000$ kg. In scientific - notation, this is close to $6\times10^{24}$ kg.

Step2: Assume Liam's mass

Let's assume Liam's mass is $1\times10^{2}$ kg (from the previous part of the problem if it's related).

Step3: Calculate the ratio

To find out how many times the Earth's mass is larger than Liam's mass, we divide the Earth's mass by Liam's mass. Let $M_E$ be the Earth's mass and $M_L$ be Liam's mass. The ratio $n=\frac{M_E}{M_L}$. Substituting $M_E = 6\times10^{24}$ kg and $M_L=1\times10^{2}$ kg, we use the rule of exponents $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$. So $n=\frac{6\times10^{24}}{1\times10^{2}}=6\times10^{24 - 2}=6\times10^{22}$.

Answer:

C. $6\times10^{22}$