jupiter is the largest planet in our solar system. it has a diameter of 9 × 10⁴ miles. the smallest planet…
jupiter is the largest planet in our solar system. it has a diameter of 9 × 10⁴ miles. the smallest planet in our solar system, mercury, has a diameter of 3 × 10³ miles. use these numbers to complete the sentence below. write your answer in standard form, without using exponents. the diameter of jupiter is times the diameter of mercury.
Answer
Explanation:
Step1: Set up the ratio
To find out how many times the diameter of Jupiter is that of Mercury, we divide the diameter of Jupiter by the diameter of Mercury. The diameter of Jupiter is $9\times10^{4}$ and of Mercury is $3\times10^{3}$. So the ratio is $\frac{9\times 10^{4}}{3\times 10^{3}}$.
Step2: Divide the coefficients and subtract exponents
Divide the coefficients $9\div3 = 3$, and for the powers of 10, use the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$, so $\frac{10^{4}}{10^{3}}=10^{4 - 3}=10^{1}$. Then $3\times10^{1}=30$.
Answer:
30