Question

task
powers of 10
the most massive planet in the solar system, jupiter, has a mass of about 1,898,000,000,000,000,000,000,000,000 kg.
the least massive planet is mercury, which has a mass of about 330,000,000,000,000,000,000,000 kg.
how many times more massive is jupiter than mercury? answer the questions to find out.
part a
estimate jupiter’s mass using a one - digit whole number times a power of 10. be sure to include units.
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part b
estimate mercury’s mass using a one - digit whole number times a power of 10. be sure to include units.
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Explanation:

Step1: Identify the masses

Jupiter's mass: \( 1,898,000,000,000,000,000,000,000,000 \, \text{kg} \)
Mercury's mass: \( 330,000,000,000,000,000,000,000 \, \text{kg} \)

Step2: Estimate the division

Estimate \( \frac{1,898 \times 10^{24}}{330 \times 10^{21}} \approx \frac{1900 \times 10^{24}}{300 \times 10^{21}} \)

Step3: Simplify the powers of 10

\( \frac{10^{24}}{10^{21}} = 10^{3} \)

Step4: Simplify the coefficients

\( \frac{1900}{300} \approx 6.33 \), round to one - digit: \( 6 \)

Step5: Combine the results

\( 6\times10^{3}=6000 \)

Answer:

Jupiter is approximately \( 6\times 10^{3} \) (or 6000) times more massive than Mercury.