To arrange the numbers in increasing order and provide their decimal approximations using \( \pi \approx 3.14 \), we first interpret the expressions:
- \( -\pi \approx -3.14 \)
- \( 1.57 \) (this is also \( \frac{\pi}{2} \approx 1.57 \))
- \( -3.14 \) (already given)
- \( \frac{\pi}{2} \approx 1.57 \) (already mentioned)
- \( \sqrt{23} \approx 4.79 \)
- \( -3.446 \) (already given)
- \( 2\pi \approx 6.28 \)
- \( \sqrt{47} \approx 6.85 \)
- \( 4.79 \) (already mentioned)
- \( 6.28 \) (already mentioned)
- \( 6.85 \) (already mentioned)
Now let's summarize them one by one.
Ordering the Numbers
- \( -\pi \approx -3.14 \)
- \( -3.446 \)
- \( -3.14 \)
- \( \frac{\pi}{2} \approx 1.57 \)
- \( 4.79 \)
- \( 2\pi \approx 6.28 \)
- \( \sqrt{47} \approx 6.85 \)
Final Ordered List
- \( -\pi \approx -3.14 \)
- \( -3.446 \approx -3.446 \)
- \( -3.14 \approx -3.14 \)
- \( \frac{\pi}{2} \approx 1.57 \)
- \( 4.79 \approx 4.79 \)
- \( 2\pi \approx 6.28 \)
- \( \sqrt{47} \approx 6.85 \)
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)