Question

Mercury: 35.9 million miles
Venus: 67.2 million miles
Earth: 93 million miles
Mars: 142 million miles
Jupiter: 483 million miles
Saturn: 885.5 million miles
Uranus: 1.8 billion miles
Neptune: 2.8 billion miles
Use this information to answer the following questions
Make a list of the distances from each planet to the sun, written in scientific notation. If there is a shortest and longest distance, use the average distance from the sun.
Choose two of the distances of planets from the sun and add them. Show your work.

Answer 1

Here are the distances from each planet to the Sun, written in scientific notation:

- Mercury: \(3.59 \times 10^7\) miles
- Venus: \(6.72 \times 10^7\) miles
- Earth: \(9.3 \times 10^7\) miles
- Mars: \(1.42 \times 10^8\) miles
- Jupiter: \(4.83 \times 10^8\) miles
- Saturn: \(8.855 \times 10^8\) miles
- Uranus: \(1.8 \times 10^9\) miles
- Neptune: \(2.8 \times 10^9\) miles

### Shortest and Longest Distance:
- The shortest distance is Mercury: \(3.59 \times 10^7\) miles.
- The longest distance is Neptune: \(2.8 \times 10^9\) miles.

### Average Distance Calculation:
To find the average distance, we'll convert the scientific notation of the distances to a common unit and then average them:

\[
\text{Average distance} = \frac{(3.59 \times 10^7) + (6.72 \times 10^7) + (9.3 \times 10^7) + (1.42 \times 10^8) + (4.83 \times 10^8) + (8.855 \times 10^8) + (1.8 \times 10^9) + (2.8 \times 10^9)}{8}
\]

Calculating the sum:
\[
= 3.59 \times 10^7 + 6.72 \times 10^7 + 9.3 \times 10^7 + 1.42 \times 10^8 + 4.83 \times 10^8 + 8.855 \times 10^8 + 1.8 \times 10^9 + 2.8 \times 10^9
\]

This works out to be:
\[
= 0.0359 + 0.0672 + 0.093 + 0.142 + 0.483 + 0.8855 + 1.8 + 2.8 \quad \text{ (in billions)}
\]

\[
= 6.5066 \times 10^9 \quad \text{ (after converting to a common base of billion)}
\]

Now, averaging:
\[
\text{Average distance} = \frac{6.5066 \times 10^9}{8} \approx 8.133 \times 10^8 \text{ miles}
\]

### Adding Two Distances:
Let’s choose the distances from Earth and Jupiter:
- Earth: \(9.3 \times 10^7\) miles
- Jupiter: \(4.83 \times 10^8\) miles

Express Jupiter in the same terms (to be compatible):
\[
4.83 \times 10^8 = 48.3 \times 10^7
\]

Now, we can add them:
\[
(9.3 \times 10^7) + (48.3 \times 10^7) = (9.3 + 48.3) \times 10^7 = 57.6 \times 10^7
\]

Converting back into scientific notation:
\[
57.6 \times 10^7 = 5.76 \times 10^8 \text{ miles}
\]

Thus, the sum of the distances from Earth and Jupiter to the Sun is \(5.76 \times 10^8\) miles.