Drag the numbers to put them in order from least value (top) to greatest value (bottom).

 

[2π,38⎯⎯⎯⎯√,4/17,5 3/4]

To arrange the numbers in order from least to greatest, let’s evaluate each one to approximate its decimal form:

1. **\(4/17\)**: approximately \(0.235\)
2. **\( \sqrt{38} \)**: approximately \(6.164\)
3. **\(2\pi\)**: approximately \(6.283\) (using \( \pi \approx 3.1416 \))
4. **\(5 \frac{3}{4}\)** or \(5.75\)

Now, in ascending order:

1. \( \frac{4}{17} \approx 0.235\)
2. \(5 \frac{3}{4} = 5.75\)
3. \( \sqrt{38} \approx 6.164\)
4. \(2\pi \approx 6.283\)

So the order from least to greatest is:

\[
\frac{4}{17}, \, 5 \frac{3}{4}, \, \sqrt{38}, \, 2\pi
\]

Would you like further details on any steps? 

Here are five related questions:

1. What is the significance of approximating irrational numbers in calculations?
2. How would we determine the order if we didn't know the value of \(\pi\) or \(\sqrt{38}\)?
3. Can you compare rational and irrational numbers in other ways besides decimals?
4. How would adding more complex numbers (e.g., imaginary numbers) affect ordering?
5. Why is it helpful to convert mixed fractions to decimal form?

**Tip:** Remember, approximations are useful but should be as precise as needed for accuracy in more complex calculations.

Drag the numbers to put them in order from least value (top) to greatest value (bottom). [2π, √38, 4/17, 5 3/4]

Learn how to arrange numbers in order from least to greatest with examples including irrational numbers like 2π and √38. This problem demonstrates decimal approximation and number comparison techniques, perfect for students in Grades 6-8.

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