Earth's radius is approximately 3,959 miles, while Jupiter's radius is approximately 4.3441×10

Question

4
miles. How much bigger is Jupiter's radius compared to Earth's?
Express your answer in scientific notation. Do not round your answer. (1 point)
____ \times ____ miles

Answer 1

To find out how much bigger Jupiter's radius is compared to Earth's, you can divide Jupiter's radius by Earth's radius:

1. Earth's radius: $R_E=3,959$ miles
2. Jupiter's radius: $R_J\approx 4.3441\times {10}^4$ miles

Now, calculate the factor by which Jupiter's radius is larger:

$$\frac{R_J}{R_E}=\frac{4.3441\times {10}^4}{3,959}$$

Performing the calculation:

$$\frac{4.3441\times {10}^4}{3,959}\approx \frac{4.3441}{3.959}\times {10}^4$$

Calculating $\frac{4.3441}{3.959}\approx 1.096$ (not rounded yet):

So:

$$\frac{R_J}{R_E}\approx 1.096\times {10}^4$$

Now, we express $1.096$ in scientific notation:

$$1.096\approx 1.096\times {10}^0$$

Therefore:

$$\frac{R_J}{R_E}\approx 1.096\times {10}^4\times {10}^0=1.096\times {10}^{4+0}=1.096\times {10}^4$$

Thus, Jupiter's radius is approximately:

$$1.096\times {10}^4\text{ miles}\text{ larger than Earth's radius.}$$

Expressing your answer in scientific notation:

$$1.096\times {10}^4$$

So the answer is:

$$1.096\times {10}^4\text{ miles}$$