Question

List the numbers shown above in the number line in increasing order.
Identify the decimal approximation below each number. Use 3.14 as an approximation for 𝜋.



-

<

Correct answer:
-𝜋
<

Incorrect answer:
1.57
<

Incorrect answer:
-3.14

<

Incorrect answer:
𝜋/2
<

Incorrect answer:
square root of 23

-3.446
<

Incorrect answer:
2𝜋
<

Incorrect answer:
square root of 47
<

4.79
<

Correct answer:
6.28
<

6.85

Answer 1

To arrange the numbers in increasing order and provide their decimal approximations using \( \pi \approx 3.14 \), we first interpret the expressions:

1. \( -\pi \approx -3.14 \)
2. \( 1.57 \) (this is also \( \frac{\pi}{2} \approx 1.57 \))
3. \( -3.14 \) (already given)
4. \( \frac{\pi}{2} \approx 1.57 \) (already mentioned)
5. \( \sqrt{23} \approx 4.79 \)
6. \( -3.446 \) (already given)
7. \( 2\pi \approx 6.28 \)
8. \( \sqrt{47} \approx 6.85 \)
9. \( 4.79 \) (already mentioned)
10. \( 6.28 \) (already mentioned)
11. \( 6.85 \) (already mentioned)

Now let's summarize them one by one.

### Ordering the Numbers

1. **\( -\pi \approx -3.14 \)**
2. **\( -3.446 \)**
3. **\( -3.14 \)**
4. **\( \frac{\pi}{2} \approx 1.57 \)**
5. **\( 4.79 \)**
6. **\( 2\pi \approx 6.28 \)**
7. **\( \sqrt{47} \approx 6.85 \)**

### Final Ordered List
1. \( -\pi \approx -3.14 \)
2. \( -3.446 \approx -3.446 \)
3. \( -3.14 \approx -3.14 \)
4. \( \frac{\pi}{2} \approx 1.57 \)
5. \( 4.79 \approx 4.79 \)
6. \( 2\pi \approx 6.28 \)
7. \( \sqrt{47} \approx 6.85 \)

Thus, the numbers in increasing order are:

- \( -\pi \) (approximately -3.14)
- \( -3.446 \)
- \( -3.14 \)
- \( \frac{\pi}{2} \) (approximately 1.57)
- \( 4.79 \)
- \( 2\pi \) (approximately 6.28)
- \( \sqrt{47} \) (approximately 6.85)