Our solar system is approximately 10 billion km across. This diameter can be also be expressed as: 10 x 10⁹ km 1010 km 1013 m All of the above. Both a and b are correct

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Chapter1: Units, Trigonometry. And Vectors
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### Understanding the Scale of Our Solar System

Our solar system is approximately 10 billion kilometers across. This diameter can also be expressed in different forms. Test your knowledge with the multiple-choice question below:

#### Question
Our solar system is approximately 10 billion km across. This diameter can be also be expressed as:

- **A.** \(10 \times 10^9\) km
- **B.** \(10^{10}\) km
- **C.** \(10^{13}\) m
- **D.** All of the above.
- **E.** Both a and b are correct

#### Explanation:

- **Option A:** \(10 \times 10^9\) km is an accurate way to express 10 billion kilometers because \(10^9\) is a billion.
- **Option B:** \(10^{10}\) km is incorrect as it represents a larger magnitude, 10 billion would simply be \(10^{10}\) not \(10^{10}\).
- **Option C:** \(10^{13}\) meters is correct since converting kilometers to meters involves multiplying by \(10^3\) (as 1 km = 1000 meters or \(10^3\) meters), so \(10^{10} \, \text{km} \times 10^3 = 10^{13} \, \text{m}\).
- **Option D:** All of the above would imply all options are correct but since B is incorrect, this option cannot be correct.
- **Option E:** This option suggests that both A and B are correct but since B is incorrect, this cannot be correct either.

#### Correct Answer: 
**A. \(10 \times 10^9\) km** and **C. \(10^{13}\) m**

Use the above information to reinforce your understanding of scientific notation and unit conversion in astronomy.
Transcribed Image Text:### Understanding the Scale of Our Solar System Our solar system is approximately 10 billion kilometers across. This diameter can also be expressed in different forms. Test your knowledge with the multiple-choice question below: #### Question Our solar system is approximately 10 billion km across. This diameter can be also be expressed as: - **A.** \(10 \times 10^9\) km - **B.** \(10^{10}\) km - **C.** \(10^{13}\) m - **D.** All of the above. - **E.** Both a and b are correct #### Explanation: - **Option A:** \(10 \times 10^9\) km is an accurate way to express 10 billion kilometers because \(10^9\) is a billion. - **Option B:** \(10^{10}\) km is incorrect as it represents a larger magnitude, 10 billion would simply be \(10^{10}\) not \(10^{10}\). - **Option C:** \(10^{13}\) meters is correct since converting kilometers to meters involves multiplying by \(10^3\) (as 1 km = 1000 meters or \(10^3\) meters), so \(10^{10} \, \text{km} \times 10^3 = 10^{13} \, \text{m}\). - **Option D:** All of the above would imply all options are correct but since B is incorrect, this option cannot be correct. - **Option E:** This option suggests that both A and B are correct but since B is incorrect, this cannot be correct either. #### Correct Answer: **A. \(10 \times 10^9\) km** and **C. \(10^{13}\) m** Use the above information to reinforce your understanding of scientific notation and unit conversion in astronomy.
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