Sara and Sam are each working on a science project in which they need to research the individual masses of the nine planets (including the dwarf planet Pluto as the ninth planet). Sara completes her data for the planets' masses in kilograms while Sam's data is in milligrams.

Question

Sara:

Planet Mass (in kilograms)
Jupiter 1.989 · 1027
Saturn 5.685 · 1026
Neptune 1.024 · 1026
Uranus 8.681 · 1025
Earth 5.974 · 1024
Venus 4.869 · 1024
Mars 6.419 · 1023
Mercury 3.302 · 1023
Pluto 1.31 · 1022
Sam:

Planet Mass (in milligrams)
Jupiter 1.989 · 1033
Saturn 5.685 · 1032
Neptune 1.024 · 1032
Uranus 8.681 · 1031
Earth 5.974 · 1030
Venus 4.869 · 1030
Mars 6.419 · 1029
Mercury 3.302 · 1029
Pluto 1.31 · 1028
Approximate how many times greater Saturn's mass is than Mercury's.

200,000
2,000,000
2,000
20,000

Answer 1

To approximate how many times greater Saturn's mass is than Mercury's, we can use the values provided by Sara or Sam.

Using Sara's data:

1. Saturn's mass = \(5.685 \times 10^{26}\) kg
2. Mercury's mass = \(3.302 \times 10^{23}\) kg

Now, we calculate the ratio of Saturn's mass to Mercury's mass:

\[ \text{Ratio} = \frac{\text{Saturn's mass}}{\text{Mercury's mass}} = \frac{5.685 \times 10^{26}}{3.302 \times 10^{23}} \]

Calculating the exponent difference:

\[ = 5.685 \times 10^{26 - 23} = 5.685 \times 10^3 \]

Now we compute this value:

\[ 5.685 \times 10^3 \approx 5685 \]

This value suggests that Saturn's mass is approximately 5685 times greater than Mercury's mass.

Now, let's check the answer choices provided:

• 200,000
• 2,000,000
• 2,000
• 20,000

The closest answer is 2,000, which roughly corresponds to our calculation when considering significant figures. Therefore, the most appropriate answer based on the options is:

2,000.