Let's analyze the question and order the numbers provided from least to greatest. We need to consider the values of these numbers in decimal form to compare them accurately.
The given numbers are:
1. [tex]\( 1 \frac{3}{4} \)[/tex] which is equal to [tex]\( 1 + \frac{3}{4} = 1.75 \)[/tex]
2. [tex]\( \sqrt{\pi} \approx 1.7724538509055159 \)[/tex]
3. [tex]\( 1.71 \)[/tex]
4. [tex]\( \frac{16}{9} \approx 1.7777777777777777 \)[/tex]
Let's list these numbers with their decimal representations:
- [tex]\( 1 \frac{3}{4} \)[/tex] = 1.75
- [tex]\( \sqrt{\pi} \approx 1.7724538509055159 \)[/tex]
- [tex]\( 1.71 \)[/tex]
- [tex]\( \frac{16}{9} \approx 1.7777777777777777 \)[/tex]
Now, we will order these numbers from least to greatest:
1. 1.71
2. 1.75 (which is [tex]\( 1 \frac{3}{4} \)[/tex])
3. [tex]\( \sqrt{\pi} \approx 1.7724538509055159 \)[/tex]
4. [tex]\( \frac{16}{9} \approx 1.7777777777777777 \)[/tex]
Let's see which answer choice matches this order:
- The first choice is: [tex]\( 1 \frac{3}{4}, \sqrt{\pi}, 1.71, \frac{16}{9} \)[/tex]
- The second choice is: [tex]\( \sqrt{\pi}, 1 \frac{3}{4}, \frac{16}{9}, 1.71 \)[/tex]
- The third choice is: [tex]\( 1.71,1 \frac{3}{4}, \sqrt{\pi}, \frac{16}{9} \)[/tex]
- The fourth choice is: [tex]\( \frac{16}{9}, 1.71, \sqrt{\pi}, 1 \frac{3}{4} \)[/tex]
Comparing these with the correct order 1.71, 1.75, [tex]\( \sqrt{\pi} \approx 1.7724538509055159 \)[/tex], [tex]\( \frac{16}{9} \approx 1.7777777777777777 \)[/tex]:
- The third choice, [tex]\( 1.71, 1 \frac{3}{4}, \sqrt{\pi}, \frac{16}{9} \)[/tex], is ordered correctly from least to greatest.
Thus, the correct answer is:
[tex]$1.71, 1 \frac{3}{4}, \sqrt{\pi}, \frac{16}{9}$[/tex]
