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Select the correct answer.

Venus is an average distance of 108.2 million kilometers from the Sun. Use the conversion factor [tex]1 \, \text{AU} = 1.5 \times 10^8 \, \text{km}[/tex] to convert this distance from kilometers to astronomical units. Choose the closest answer.

A. [tex]0.72 \, \text{AU}[/tex]
B. [tex]1.25 \, \text{AU}[/tex]
C. [tex]3.56 \, \text{AU}[/tex]
D. [tex]45.63 \, \text{AU}[/tex]
E. [tex]96.12 \, \text{AU}[/tex]



Answer :

GinnyAnswer
To convert the average distance of Venus from the Sun, given in kilometers, to astronomical units (AU), we need to use the given conversion factor.

The given data:
- Distance of Venus from the Sun: 108.2 million kilometers
- Conversion factor: [tex]\(1 \text{ AU} = 1.5 \times 10^8 \text{ km}\)[/tex]

Step-by-Step Solution:

1. Identify the distance in kilometers:
[tex]\[ \text{Distance in km} = 108.2 \times 10^6 \text{ km} \][/tex]

2. Identify the conversion factor:
[tex]\[ 1 \text{ AU} = 1.5 \times 10^8 \text{ km} \][/tex]

3. Set up the conversion calculation:
To find the distance in astronomical units (AU), divide the distance in kilometers by the conversion factor:
[tex]\[ \text{Distance in AU} = \frac{\text{Distance in km}}{\text{Conversion factor}} \][/tex]

4. Perform the calculation:
[tex]\[ \text{Distance in AU} = \frac{108.2 \times 10^6 \text{ km}}{1.5 \times 10^8 \text{ km}} \][/tex]

5. Simplify the calculation:
[tex]\[ \text{Distance in AU} = \frac{108.2}{1.5} \times \frac{10^6}{10^8} \][/tex]
[tex]\[ \text{Distance in AU} = \frac{108.2}{1.5} \times 10^{-2} \][/tex]
[tex]\[ \text{Distance in AU} = 72.13333333333334 \times 10^{-2} \][/tex]
[tex]\[ \text{Distance in AU} = 0.7213333333333334 \text{ AU} \][/tex]

In conclusion, the distance of Venus from the Sun in astronomical units is approximately [tex]\(0.721 \text{ AU}\)[/tex].

Therefore, the closest answer is:
[tex]\[ \boxed{0.72 \text{ AU}} \][/tex]

So the correct choice is:
[tex]\[ \text{A. } 0.72 \text{ AU} \][/tex]

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