You're correct in pointing out that $\sqrt{7}$ isn't a whole number. However, it does exist as an irrational number. The square root of 7 ($\sqrt{7}$) is an irrational number that approximately equals 2.64575.

In this problem, you're supposed to order all the numbers from least to greatest, including $\sqrt{7}$ even though it's an irrational number. Here's the revised ordering explanation:

1. $\frac{2}{3}$ = $0.6666...$ (approximately 0.67)
2. 2.2 (already a decimal)
3. $\sqrt{4}$ = 2 (since $\sqrt{4} = 2$)
4. $\sqrt{7}$ ≈ 2.64575
5. 2.3 (already a decimal)

So, from least to greatest, the correct order is:

$\frac{2}{3}, \sqrt{4}, 2.2, 2.3, \sqrt{7}$

Would you like any more details or explanations?

---

Related questions:

1. What is the approximate value of $\sqrt{2}$?
2. How can you determine if a number is irrational?
3. What is the square root of 9?
4. How can you simplify square roots?
5. What is the difference between rational and irrational numbers?

Tip: Remember that square roots of non-perfect squares (like $\sqrt{7}$) are irrational numbers and cannot be exactly expressed as fractions or decimals.