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This activity is about identifying rational and irrational numbers. 

Here's a quick summary of the types:
- **Rational Numbers**: Can be expressed as a fraction \(\frac{a}{b}\), where \(a\) and \(b\) are integers and \(b \neq 0\). Examples include integers, fractions, and terminating or repeating decimals.
- **Irrational Numbers**: Cannot be written as a fraction of two integers. Their decimal expansions are non-repeating and non-terminating. Examples include \(\sqrt{2}\), \(\pi\), and \(\sqrt{5}\).

I'll help categorize the numbers shown in the worksheet. Here’s how each term sorts:

1. **Irrational Numbers**:
   - \(\sqrt{2}\), \(\pi\), \(\sqrt{21}\), \(\sqrt{22}\), \(\sqrt{60}\), \(\sqrt{125}\), and \(\sqrt{81}\) if not a perfect square, as these roots generally don’t simplify to rational numbers.
   
2. **Rational Numbers**:
   - \( \frac{5}{4} \), \( -3\pi \) (if it’s intended to be rational, otherwise irrational), \(-2\), \(0.72\), \(-0.975\), \(-4.9\), \(4\), \(5.083\), \(\frac{6}{8}\), \( \frac{1}{100} \), \(-\frac{3}{8}\), \(8.7032\), \(0.3\), and \(\sqrt{8}\) (if it simplifies to a fraction).

Let me know if you need a more detailed answer for any specific number on the list! 

### Questions for Further Practice
1. Why is \(\pi\) considered irrational, and are there other similar constants?
2. Can a decimal that terminates be irrational? Why or why not?
3. How would you identify whether a square root is rational or irrational?
4. What are examples of rational numbers in fraction form that appear complex but simplify to integers?
5. How does repeating versus non-repeating in decimals relate to rationality?

**Tip**: For quick classification, check if the decimal repeats or if a square root simplifies to an integer; both indicate rationality.

Classify each number in the image as rational or irrational using the key provided.

Learn how to classify numbers as rational or irrational with this worksheet solution. This exercise helps students understand the difference between rational and irrational numbers through examples like square roots and fractions. Suitable for Grade 8 math students.

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