Question

the sun is about 1.39×10^6 km in diameter. a certain asteroid is about 2.0×10^3 km in diameter. about how many times larger is the suns diameter than the asteroids? d. 7.0×10^2 c. 6.95×10^(-3) a b 6.95×10^9 6.95×10^2 c d

Explanation:

Step1: Set up the division

To find out how many times larger the Sun's diameter is than the asteroid's, we divide the Sun's diameter by the asteroid's diameter. The Sun's diameter is $1.39\times 10^{6}$ km and the asteroid's diameter is $2.0\times 10^{3}$ km. So the calculation is $\frac{1.39\times 10^{6}}{2.0\times 10^{3}}$.

Step2: Divide the coefficients and subtract the exponents

First, divide the coefficients: $\frac{1.39}{2.0}= 0.695$. Then, use the rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, so $\frac{10^{6}}{10^{3}}=10^{6 - 3}=10^{3}$.

Step3: Combine the results

Multiply the result of the coefficient - division by the result of the exponent - operation: $0.695\times10^{3}$. In scientific notation, we want the coefficient to be between 1 and 10. So we rewrite $0.695\times10^{3}$ as $6.95\times10^{2}$ (since $0.695\times10^{3}=(6.95\times10^{- 1})\times10^{3}=6.95\times10^{-1 + 3}=6.95\times10^{2}$).

Answer:

D. $6.95\times 10^{2}$