Question

the mass of the sun is 1×10^{30} kilograms. the mass of the earth is 5×10^{24} kilograms. how many times bigger is the sun than the earth? 1. 2×10^{5} 2. 2×10^{6} 3. 5×10^{6} 4. 4×10^{30}

Explanation:

Step1: Set up the ratio

To find out how many times bigger the sun's mass is than the earth's mass, we divide the mass of the sun by the mass of the earth. The mass of the sun is $1\times10^{30}$ kg and the mass of the earth is $5\times 10^{24}$ kg. So the ratio is $\frac{1\times 10^{30}}{5\times 10^{24}}$.

Step2: Use the quotient - rule of exponents

The quotient - rule of exponents states that $\frac{a^m}{a^n}=a^{m - n}$ and $\frac{a}{b}\times\frac{10^m}{10^n}=\frac{a}{b}\times10^{m - n}$. Here, $\frac{1}{5}\times\frac{10^{30}}{10^{24}}$. First, $\frac{1}{5}=0.2$, and $\frac{10^{30}}{10^{24}} = 10^{30-24}=10^{6}$. Then $0.2\times10^{6}$.

Step3: Convert to scientific notation

We know that $0.2=\ 2\times10^{-1}$, so $0.2\times10^{6}=2\times10^{-1}\times10^{6}$. Using the product - rule of exponents $a^m\times a^n=a^{m + n}$, we get $2\times10^{-1 + 6}=2\times10^{5}$.

Answer:

A. $2\times 10^{5}$