Question

The mass of the Sun is approximately 1.989 x 10^30
kilograms, while the mass of Jupiter is about 1.898 x 10^27
kilograms.

Which answer is closest to the difference between the mass of the Sun and the mass of Jupiter?

Answer 1

To find the difference between the mass of the Sun and the mass of Jupiter, you can subtract the mass of Jupiter from the mass of the Sun:

\[
\text{Mass of the Sun} - \text{Mass of Jupiter} = (1.989 \times 10^{30} \text{ kg}) - (1.898 \times 10^{27} \text{ kg})
\]

Since the mass of the Sun is significantly larger than the mass of Jupiter, we can approximate this calculation by simplifying the numbers. First, we can express the mass of Jupiter in terms of \(10^{30}\):

\[
1.898 \times 10^{27} \text{ kg} = 0.001898 \times 10^{30} \text{ kg}
\]

Now, we perform the subtraction:

\[
1.989 \times 10^{30} \text{ kg} - 0.001898 \times 10^{30} \text{ kg} \approx 1.989 \times 10^{30} \text{ kg}
\]

Now calculating the precise difference:

\[
1.989 \times 10^{30} \text{ kg} - 0.001898 \times 10^{30} \text{ kg} = (1.989 - 0.001898) \times 10^{30} \text{ kg}
\]
\[
= 1.987102 \times 10^{30} \text{ kg}
\]

So the mass difference is approximately:

\[
1.987102 \times 10^{30} \text{ kg}
\]

The difference is very close to the mass of the Sun itself. Thus, the closest answer to the difference between the mass of the Sun and the mass of Jupiter is approximately:

\[
1.987 \times 10^{30} \text{ kg}
\]