To order the numbers from least to greatest, we first convert them to their decimal equivalents:

1. $\frac{1}{4} = 0.25$
2. $-3 = -3.00$
3. $\sqrt{3} \approx 1.732$
4. $-\frac{3}{2} = -1.5$
5. $3.8 = 3.8$

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

$-3, -\frac{3}{2}, \frac{1}{4}, \sqrt{3}, 3.8$

So the order is:

$-3, -\frac{3}{2}, \frac{1}{4}, \sqrt{3}, 3.8$

Would you like more details or have any questions?

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Here are five related questions:

1. How do you convert fractions to decimals?
2. What is the approximate value of $\sqrt{2}$?
3. How do you compare irrational numbers like $\sqrt{3}$ to rational numbers?
4. What are the rules for ordering negative and positive numbers?
5. How can you estimate the value of $\sqrt{5}$ without a calculator?

Tip: When ordering numbers, it can be helpful to convert all the numbers to the same form, such as decimals, to make comparisons easier.