Let's analyze and compare the given numbers to determine their correct order from least to greatest.
1. Number 1: [tex]\( 1 \frac{3}{4} \)[/tex]
- As a decimal: [tex]\( 1 \frac{3}{4} = 1 + \frac{3}{4} = 1.75 \)[/tex]
2. Number 2: [tex]\( \sqrt{\pi} \)[/tex]
- We can approximate [tex]\( \pi \approx 3.14159 \)[/tex]
- Therefore, [tex]\( \sqrt{\pi} \approx \sqrt{3.14159} \approx 1.772 \)[/tex]
3. Number 3: [tex]\( 1.71 \)[/tex]
- Already in decimal form: [tex]\( 1.71 \)[/tex]
4. Number 4: [tex]\( \frac{16}{9} \)[/tex]
- As a decimal: [tex]\( \frac{16}{9} \approx 1.778 \)[/tex]
Next, we compare these decimal values:
- [tex]\( 1.71 \)[/tex]
- [tex]\( 1.75 \)[/tex]
- [tex]\( \sqrt{\pi} \approx 1.772 \)[/tex]
- [tex]\( \frac{16}{9} \approx 1.778 \)[/tex]
Now we arrange them from least to greatest:
1. [tex]\( 1.71 \)[/tex]
2. [tex]\( 1.75 \)[/tex]
3. [tex]\( \sqrt{\pi} \approx 1.772 \)[/tex]
4. [tex]\( \frac{16}{9} \approx 1.778 \)[/tex]
Let's identify the correct answer choice:
1. [tex]\( 1 \frac{3}{4}, \sqrt{\pi}, 1.71, \frac{16}{9} \)[/tex]
2. [tex]\( \sqrt{\pi}, 1 \frac{3}{4}, \frac{16}{9}, 1.71 \)[/tex]
3. [tex]\( 1.71, 1 \frac{3}{4}, \sqrt{\pi}, \frac{16}{9} \)[/tex]
4. [tex]\( \frac{16}{9}, 1.71, \sqrt{\pi}, 1 \frac{3}{4} \)[/tex]
The correct answer choice that matches the order [tex]\( 1.71, 1.75, \sqrt{\pi}, \frac{16}{9} \)[/tex] is:
[tex]\[ \boxed{3} \][/tex]
