To convert the distance from kilometers to Astronomical Units (AU), we need to know that 1 AU is approximately equal to 149.6 million kilometers.
Here’s a step-by-step solution to find the distance of Neptune from the sun in AU:
1. Identify the given distance in kilometers:
The distance from Neptune to the Sun is 4.5 billion kilometers.
2. Understand the conversion factor:
1 AU is approximately 149.6 million kilometers.
3. Set up the conversion calculation:
To convert the distance from kilometers to AU, we use the following relationship:
[tex]\[
1 \text{ AU} = 149,600,000 \text{ kilometers}
\][/tex]
4. Convert the distance to standard form for clarity:
4.5 billion kilometers can be written as 4.5e9 kilometers.
5. Perform the division to convert kilometers to AU:
[tex]\[
\text{Distance in AU} = \frac{4.5 \text{ billion kilometers}}{149.6 \text{ million kilometers per AU}}
\][/tex]
6. Simplify the numerical values:
[tex]\[
4.5 \times 10^9 \text{ kilometers divided by } 149.6 \times 10^6 \text{ kilometers per AU}
\][/tex]
7. Calculate the distance in AU:
[tex]\[
\text{Distance in AU} = \frac{4.5 \times 10^9}{149.6 \times 10^6} = \frac{4500 \times 10^6}{149.6 \times 10^6}
\][/tex]
8. Simplify the ratio:
[tex]\[
\text{Distance in AU} = \frac{4500}{149.6} \approx 30.08
\][/tex]
Thus, the distance from Neptune to the Sun is approximately \(30.08\) AU.
Among the given options:
- [tex]$0.3 AU$[/tex]
- 3.8 AU
- [tex]$30 AU$[/tex]
- 3 million [tex]$AU$[/tex]
The most accurate choice is [tex]\(30 AU\)[/tex].
