Earth is approximately 5 times 10 Superscript 9 years old. For which of these ages could this be an​ approximation?
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Part 1
Select all that apply.
A.
4.919999999 times 10 Superscript 9 years
B.
4 comma 583 comma 700 comma 000 years
C.
50 comma 000 comma 000 comma 000 years
D.
3.69 times 10 Superscript 9 years
E.
4 comma 762 comma 000 comma 000 years

To determine which of these ages could be approximated to \(5 \times 10^9\) years, we need to evaluate each option to see if it is reasonably close to this value.

Let's evaluate each option:

1. **Option A: \(4.919999999 \times 10^9\) years**

   \[
   4.919999999 \times 10^9 = 4.92 \times 10^9 \, \text{years}
   \]

   This value is very close to \(5 \times 10^9\) years, so it is a possible approximation.

2. **Option B: 4,583,700,000 years**

   Convert this to scientific notation:

   \[
   4,583,700,000 = 4.5837 \times 10^9 \, \text{years}
   \]

   This is also reasonably close to \(5 \times 10^9\) years, so it is a possible approximation.

3. **Option C: 50,000,000,000 years**

   Convert this to scientific notation:

   \[
   50,000,000,000 = 5 \times 10^{10} \, \text{years}
   \]

   This value is much larger than \(5 \times 10^9\) years (10 times larger), so it is not a reasonable approximation.

4. **Option D: \(3.69 \times 10^9\) years**

   This value is smaller than \(5 \times 10^9\) years. However, it is more than 1 billion years off from \(5 \times 10^9\), so it is not a reasonable approximation.

5. **Option E: 4,762,000,000 years**

   Convert this to scientific notation:

   \[
   4,762,000,000 = 4.762 \times 10^9 \, \text{years}
   \]

   This value is also reasonably close to \(5 \times 10^9\) years, so it could be a possible approximation.

### Conclusion:

The ages that could be approximated to \(5 \times 10^9\) years are:
- **A.** \(4.919999999 \times 10^9\) years
- **B.** 4,583,700,000 years
- **E.** 4,762,000,000 years

These are close enough to \(5 \times 10^9\) to be considered reasonable approximations.

Would you like more details, or do you have any questions?

Here are some related questions you might find interesting:
1. How is scientific notation used to simplify the representation of very large or small numbers?
2. What are the rules for rounding numbers in scientific notation?
3. How do you determine if one number is a reasonable approximation of another?
4. Why might approximations be useful in science, especially when dealing with astronomical figures?
5. What is the significance of Earth's age in the context of geological time scales?

**Tip:** When comparing large numbers, converting them to scientific notation can make it easier to see which are close to each other.

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. 4.919999999 times 10 Superscript 9 years B. 4,583,700,000 years C. 50,000,000,000 years D. 3.69 times 10 Superscript 9 years E. 4,762,000,000 years

Explore how to approximate Earth's age, given as 5 × 10^9 years, using scientific notation. This problem helps students compare numbers like 4.919999999 × 10^9 and 4,583,700,000 years, applying rules for rounding and approximation. Suitable for Grades 6-8.

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