Question

Earh’s radius is approximately 3,959 miles, while Jupiter’s radius is approximately 4.3441×104 miles. How much bigger is Jupiter’s radius compared to Earth’s? Express your answer in scientific notation. Do not round your answer.

Answer 1

To find how much bigger Jupiter's radius is compared to Earth's radius, we can divide Jupiter's radius by Earth's radius.

1. Jupiter's radius (J) = \( 4.3441 \times 10^4 \) miles
2. Earth's radius (E) = 3,959 miles

Now, we compute the ratio:

\[
\text{Ratio} = \frac{J}{E} = \frac{4.3441 \times 10^4}{3959}
\]

To perform the division, we first convert Earth’s radius into scientific notation:

\[
3959 = 3.959 \times 10^3
\]

Now substituting this back into the ratio:

\[
\text{Ratio} = \frac{4.3441 \times 10^4}{3.959 \times 10^3}
\]

Next, we can divide the coefficients and subtract the exponents:

\[
\text{Ratio} = \frac{4.3441}{3.959} \times 10^{4 - 3}
\]

Calculating \( \frac{4.3441}{3.959} \):

\[
\frac{4.3441}{3.959} \approx 1.0968
\]

So,

\[
\text{Ratio} \approx 1.0968 \times 10^1
\]

Now we can express that in scientific notation:

\[
\text{Ratio} = 1.0968 \times 10^1
\]

Thus, Jupiter's radius is approximately:

\[
**1.0968 \times 10^1** \text{ times bigger than Earth's radius.}
\]