The problem is asking to arrange five numbers in order from least to greatest:

• $3.14$
• $\frac{2}{3} \pi$
• $\pi$
• $\sqrt{3}$
• $\sqrt{3.1}$

Let’s break down each number for comparison:

1. $3.14$ is approximately $3.14$.
2. $\frac{2}{3} \pi$ is $\frac{2}{3} \times 3.1416 \approx 2.094$.
3. $\pi$ is approximately $3.1416$.
4. $\sqrt{3}$ is the square root of 3, approximately $1.732$.
5. $\sqrt{3.1}$ is the square root of 3.1, approximately $1.763$.

Now, let's compare them in order from least to greatest:

1. $\sqrt{3} \approx 1.732$
2. $\sqrt{3.1} \approx 1.763$
3. $\frac{2}{3} \pi \approx 2.094$
4. $3.14$
5. $\pi \approx 3.1416$

Thus, the correct order from least to greatest is:

• $\sqrt{3}$, $\sqrt{3.1}$, $\frac{2}{3} \pi$, $3.14$, $\pi$

Looking at the options, this corresponds to Option D.

Would you like further details or clarification on any part of this? Here are some related questions you might find useful:

1. How do you calculate square roots and approximate irrational numbers?
2. How do you compare fractions and irrational numbers more effectively?
3. What is the exact value of $\pi$ and how is it used in different contexts?
4. Can we approximate irrational numbers for practical use? How accurate should we be?
5. Why is it important to understand approximations in mathematical expressions?

Tip: When comparing numbers with square roots and irrational numbers, always try to convert them into decimal form for easier comparison.