To convert the distance of Venus from kilometers to astronomical units (AU), we can follow a sequence of clear, logical steps:
1. Understand the given data:
- Venus is 108.2 million kilometers from the Sun.
- The conversion factor is [tex]\(1 \text{ AU} = 1.5 \times 10^8 \text{ km}\)[/tex].
2. Express the distance of Venus in scientific notation:
- The distance is given as [tex]\(108.2 \text{ million kilometers} \)[/tex], which can be written as [tex]\( 108.2 \times 10^6 \text{ km} \)[/tex].
3. Apply the conversion factor:
- To convert kilometers to astronomical units, we need to divide the distance in kilometers by the distance equivalent to one astronomical unit.
- Therefore,
[tex]\[
\text{Distance in AU} = \frac{\text{Distance in kilometers}}{1.5 \times 10^8 \text{ km}}
\][/tex]
4. Perform the division:
- Plug in the given values:
[tex]\[
\text{Distance in AU} = \frac{108.2 \times 10^6 \text{ km}}{1.5 \times 10^8 \text{ km}}
\][/tex]
- Simplify the exponent terms first:
[tex]\[
\frac{108.2 \times 10^6}{1.5 \times 10^8} = \frac{108.2}{1.5} \times \frac{10^6}{10^8}
\][/tex]
- Further simplifying,
[tex]\[
\frac{108.2}{1.5} \times 10^{6-8} = \frac{108.2}{1.5} \times 10^{-2}
\][/tex]
- Perform the division:
[tex]\[
\frac{108.2}{1.5} \approx 72.1333
\][/tex]
- Finally adjust for the power of 10:
[tex]\[
72.1333 \times 10^{-2} = 0.721333
\][/tex]
5. Conclusion:
- Therefore, the distance of Venus from the Sun in astronomical units is approximately [tex]\(0.721333 \text{ AU}\)[/tex].
Given the available choices, the closest answer to 0.721333 AU would be the correct one.
