Select The Correct Answer.Venus Is An Average Distance Of 108.2 Million Kilometers From The Sun. Use The Conversion Factor $1 \text{ AU} = 1.5 \times 10^8 \text{ Km}$ To Convert This Distance From Kilometers To Astronomical Units. Choose The

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Understanding the Problem

Venus is an average distance of 108.2 million kilometers from the Sun. To convert this distance from kilometers to astronomical units (AU), we need to use the given conversion factor: $1 \text{ AU} = 1.5 \times 10^8 \text{ km}$

Step 1: Understanding the Conversion Factor

The conversion factor is given as $1 \text{ AU} = 1.5 \times 10^8 \text{ km}$ This means that 1 astronomical unit (AU) is equal to 150 million kilometers.

Step 2: Converting Distance from Kilometers to Astronomical Units

To convert the distance from kilometers to astronomical units, we need to divide the distance in kilometers by the conversion factor.

Distance in AU=Distance in kmConversion Factor\text{Distance in AU} = \frac{\text{Distance in km}}{\text{Conversion Factor}}

Distance in AU=108.2×106 km1.5×108 km/AU\text{Distance in AU} = \frac{108.2 \times 10^6 \text{ km}}{1.5 \times 10^8 \text{ km/AU}}

Step 3: Simplifying the Expression

To simplify the expression, we can divide the numerator and denominator by their greatest common divisor, which is 10610^6.

Distance in AU=108.21.5×102\text{Distance in AU} = \frac{108.2}{1.5 \times 10^2}

Distance in AU=108.2150\text{Distance in AU} = \frac{108.2}{150}

Step 4: Evaluating the Expression

To evaluate the expression, we can divide 108.2 by 150.

Distance in AU=0.7213\text{Distance in AU} = 0.7213

Conclusion

Therefore, the average distance of Venus from the Sun is approximately 0.7213 astronomical units.

Answer

The correct answer is 0.7213.

Discussion

This problem requires the use of a conversion factor to convert a distance from kilometers to astronomical units. The conversion factor is given as $1 \text{ AU} = 1.5 \times 10^8 \text{ km}$ We can use this conversion factor to convert the distance from kilometers to astronomical units by dividing the distance in kilometers by the conversion factor.

Example Use Case

This problem can be used as an example of how to convert a distance from kilometers to astronomical units. It can also be used to demonstrate the use of conversion factors in scientific calculations.

Key Concepts

  • Conversion factors
  • Astronomical units (AU)
  • Distance conversion

Mathematical Operations

  • Division
  • Simplification of expressions

Real-World Applications

  • Astronomy
  • Space exploration
  • Scientific calculations
    Q&A: Converting Distance from Kilometers to Astronomical Units ===========================================================

Frequently Asked Questions

Q: What is the conversion factor for astronomical units (AU) to kilometers?

A: The conversion factor is given as $1 \text{ AU} = 1.5 \times 10^8 \text{ km}$

Q: How do I convert a distance from kilometers to astronomical units?

A: To convert a distance from kilometers to astronomical units, you need to divide the distance in kilometers by the conversion factor.

Q: What is the average distance of Venus from the Sun in astronomical units?

A: The average distance of Venus from the Sun is approximately 0.7213 astronomical units.

Q: How do I simplify an expression when converting a distance from kilometers to astronomical units?

A: To simplify an expression, you can divide the numerator and denominator by their greatest common divisor.

Q: What is the greatest common divisor of 108.2 and 1.5 x 10^8?

A: The greatest common divisor of 108.2 and 1.5 x 10^8 is 10^6.

Q: How do I evaluate an expression when converting a distance from kilometers to astronomical units?

A: To evaluate an expression, you can divide the numerator by the denominator.

Q: What is the result of dividing 108.2 by 150?

A: The result of dividing 108.2 by 150 is 0.7213.

Q: What is the correct answer to the problem?

A: The correct answer is 0.7213.

Q: What is the use of conversion factors in scientific calculations?

A: Conversion factors are used to convert units from one system to another, making it easier to perform calculations and compare results.

Q: What are some real-world applications of converting distance from kilometers to astronomical units?

A: Some real-world applications include astronomy, space exploration, and scientific calculations.

Q: What are some key concepts related to converting distance from kilometers to astronomical units?

A: Some key concepts include conversion factors, astronomical units (AU), distance conversion, division, and simplification of expressions.

Q: What are some mathematical operations involved in converting distance from kilometers to astronomical units?

A: Some mathematical operations involved include division, simplification of expressions, and evaluation of expressions.

Q: What are some common mistakes to avoid when converting distance from kilometers to astronomical units?

A: Some common mistakes to avoid include incorrect use of conversion factors, incorrect simplification of expressions, and incorrect evaluation of expressions.

Q: How can I practice converting distance from kilometers to astronomical units?

A: You can practice by using online calculators, working through sample problems, and taking online courses or tutorials.

Q: What are some resources available for learning more about converting distance from kilometers to astronomical units?

A: Some resources available include online tutorials, textbooks, and online courses.