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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. 0.72 AU
B. 1.25 AU
C. 3.56 AU
D. 45.63 AU
E. 96.12 AU


Sagot :

Let's solve the problem step-by-step.

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

2. Convert the distance from kilometers to astronomical units (AU):
- Given distance in kilometers is [tex]\(108.2 \times 10^6 \text{ km}\)[/tex].
- Conversion factor is [tex]\(1.5 \times 10^8 \text{ km/AU}\)[/tex].

3. Set up the conversion:
To find the distance in AU, we divide the distance in kilometers by the conversion factor.
[tex]\[ \text{Distance in AU} = \frac{108.2 \times 10^6 \text{ km}}{1.5 \times 10^8 \text{ km/AU}} \][/tex]

4. Perform the division:
[tex]\[ \text{Distance in AU} = \frac{108200000}{150000000} \][/tex]
Simplifying the fraction, we get:
[tex]\[ \text{Distance in AU} \approx 0.7213 \][/tex]

5. Compare with the given options:
- A. 0.72 AU
- B. 1.25 AU
- C. 3.56 AU
- D. 45.63 AU
- E. 96.12 AU

6. Select the closest answer:
The calculated distance is [tex]\(0.7213 \text{ AU}\)[/tex], which is very close to [tex]\(0.72 \text{ AU}\)[/tex].

Hence, the correct answer is:

A. 0.72 AU