List the numbers shown above in the number line in increasing order.

Question

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)