Question

The approximate average distances from the sun to Saturn and Jupiter are listed below:
Saturn: 1, point, 4, 3, times, 10, to the power 9

kilometers
Jupiter: 7, point, 7, 8, times, 10, to the power 8

kilometers
How many times farther from the sun is Saturn? Write your answer in standard notation, rounding to the nearest tenth.

Answer 1

To find how many times farther Saturn is from the sun than Jupiter, we need to divide the distance of Saturn by the distance of Jupiter.

The distances are:
- Saturn: \( 1.43 \times 10^9 \) kilometers
- Jupiter: \( 7.78 \times 10^8 \) kilometers

Now, we set up the division:

\[
\frac{1.43 \times 10^9}{7.78 \times 10^8}
\]

To simplify this, we divide the coefficients and subtract the exponents (using the property of exponents \( \frac{10^a}{10^b} = 10^{a-b} \)):

\[
\frac{1.43}{7.78} \times 10^{9 - 8} = \frac{1.43}{7.78} \times 10^1
\]

Now, we calculate \( \frac{1.43}{7.78} \):

\[
\frac{1.43}{7.78} \approx 0.183
\]

Next, we multiply this by \( 10^1 = 10 \):

\[
0.183 \times 10 = 1.83
\]

Finally, rounding \( 1.83 \) to the nearest tenth results in:

\[
\boxed{1.8}
\]

So, Saturn is approximately 1.8 times farther from the sun than Jupiter.