Earth is approximately 5 times 10 Superscript 9 years old. For which of these ages could this be an​ approximation?
Select all that apply.
A.
4.669999999 times 10 Superscript 9 years
B.
4,527,600,000 years
C.
4.36 times 10 Superscript 9 years
D.
45,000,000,000 years
E.
4,791,000,000 years

To determine which ages could be approximated as \(5 \times 10^9\) years, we need to check if each option is close to this value.

Here's the evaluation of each option:

**A. \(4.669999999 \times 10^9\) years:**
- This value is \(4.67 \times 10^9\) years, which is close to \(5 \times 10^9\).  
- This is a valid approximation.

**B. \(4,527,600,000\) years:**
- Converting this to scientific notation: \(4.5276 \times 10^9\) years.
- This value is close to \(5 \times 10^9\).  
- This is a valid approximation.

**C. \(4.36 \times 10^9\) years:**
- This value is \(4.36 \times 10^9\) years, which is relatively close to \(5 \times 10^9\).  
- This is a valid approximation.

**D. \(45,000,000,000\) years:**
- Converting this to scientific notation: \(4.5 \times 10^{10}\) years.
- This value is much larger than \(5 \times 10^9\).  
- This is **not** a valid approximation.

**E. \(4,791,000,000\) years:**
- Converting this to scientific notation: \(4.791 \times 10^9\) years.
- This value is close to \(5 \times 10^9\).  
- This is a valid approximation.

**Correct answers: A, B, C, and E.**

Would you like more details or have any questions?

Here are some related questions for further exploration:
1. How do you convert a number into scientific notation?
2. What is the acceptable range for approximations in scientific calculations?
3. How do you determine if a number is an approximation of another?
4. How do scientific notations help in comparing very large or small numbers?
5. Why is it important to approximate values in scientific calculations?

**Tip:** When approximating, consider the significant figures and the context to decide if two numbers are close enough!

Earth is approximately 5 times 10 Superscript 9 years old. For which of these ages could this be an​ approximation? Select all that apply. A. 4.669999999 times 10 Superscript 9 years B. 4,527,600,000 years C. 4.36 times 10 Superscript 9 years D. 45,000,000,000 years E. 4,791,000,000 years

Discover how to approximate Earth's age, around 5 × 10^9 years, with a step-by-step evaluation of different values. This math problem covers scientific notation, significant figures, and approximation techniques, suitable for high school students in Grades 9-12.

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