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To solve the problem of ordering the numbers from least to greatest, let's convert each expression into its decimal form:

1. \( \sqrt{40} \):  
   \( \sqrt{40} \approx 6.324 \)

2. \( \frac{13}{2} \):  
   \( \frac{13}{2} = 6.5 \)

3. \( \frac{6}{4} \):  
   \( \frac{6}{4} = 1.5 \)

4. \( \frac{1}{4} \):  
   \( \frac{1}{4} = 0.25 \)

Now that we have the decimal values:
- \( \frac{1}{4} = 0.25 \)
- \( \frac{6}{4} = 1.5 \)
- \( \sqrt{40} \approx 6.324 \)
- \( \frac{13}{2} = 6.5 \)

The numbers in order from least to greatest are:
\[
\frac{1}{4}, \frac{6}{4}, \sqrt{40}, \frac{13}{2}
\]

Would you like further details or explanations on any part of this?

Here are 5 related questions to consider:
1. What is the square root of 50, and how would it compare in size to the numbers above?
2. How do you approximate square roots without a calculator?
3. What other methods can be used to order fractions and roots besides converting them to decimals?
4. How does \( \sqrt{40} \) relate to the simplest radical form?
5. Can you express \( \frac{6}{4} \) in simplest form?

**Tip:** When comparing different types of numbers like fractions and square roots, converting them to decimals can make it easier to order them.

Order the following numbers from least to greatest: √40, 13/2, 6/4, 1/4

Learn how to order numbers that include square roots and fractions, like √40, 13/2, 6/4, and 1/4. This problem involves converting fractions to decimals and estimating square roots. Suitable for Grades 6-8.

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