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.
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