Worksheet for classifying numbers as rational or irrational, including π, √121, and 0.333...

Let's solve this step by step.

We are given a list of numbers and need to classify each as Rational or Irrational.

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🔹 Definitions:

- Rational Numbers: Can be written as a fraction (ratio of two integers), have terminating or repeating decimal expansions.
- Irrational Numbers: Cannot be written as a simple fraction, have non-repeating, non-terminating decimals.

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🔍 Let's analyze each number:

1. 3.14
→ This is a terminating decimal, so it’s rational.
✔ Rational

2. 0.444
→ Terminating decimal → rational
✔ Rational

3. √121
→ √121 = 11 (perfect square) → integer → rational
✔ Rational

4. √1000
→ √1000 ≈ 31.622..., not a perfect square, and non-repeating → irrational
✘ Irrational

5. π
→ Famous irrational number → irrational
✘ Irrational

6. π/7
→ π is irrational; dividing it by 7 (a rational number) still gives an irrational number.
→ Irrational
✘ Irrational

7. 0.333...
→ Repeating decimal → can be written as 1/3 → rational
✔ Rational

8. 1.12313...
→ The ellipsis (...) suggests non-repeating, non-terminating (no pattern shown).
→ Likely irrational (not repeating, no clear pattern)
✘ Irrational

9. 0.12̅ (i.e., 0.121212...)
→ Repeating decimal → rational
✔ Rational

10. e
→ Euler’s number, known to be irrational
✘ Irrational

11. ∛9 (cube root of 9)
→ 9 is not a perfect cube → ∛9 ≈ 2.08..., non-repeating → irrational
✘ Irrational

12. 2.9̅ (i.e., 2.9999...)
→ Repeating decimal → rational
(Note: 2.9̅ = 3, actually!)
✔ Rational

13. 2e
→ e is irrational, multiplying by 2 (rational) → still irrational
✘ Irrational

14. 1.234̅ (i.e., 1.234234234...)
→ Repeating decimal → rational
✔ Rational

15. ∛8
→ ∛8 = 2 → perfect cube → integer → rational
✔ Rational

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✔ Final Classification:

#### Rational Numbers:
- 3.14
- 0.444
- √121 = 11
- 0.333...
- 0.12̅
- 2.9̅
- 1.234̅
- ∛8 = 2

✔ 8 Rational numbers

#### Irrational Numbers:
- √1000
- π
- π/7
- 1.12313... (non-repeating)
- e
- ∛9
- 2e

✔ 7 Irrational numbers

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📊 Fill in the Table:

#### Rational Column (8 boxes):
```
3.14
0.444
√121
0.333...
0.12̅
2.9̅
1.234̅
∛8
```

#### Irrational Column (7 boxes):
```
√1000
π
π/7
1.12313...
e
∛9
2e
```

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✔ Answer Summary:

| Rational | Irrational |
|--------|------------|
| 3.14 | √1000 |
| 0.444 | π |
| √121 | π/7 |
| 0.333... | 1.12313... |
| 0.12̅ | e |
| 2.9̅ | ∛9 |
| 1.234̅ | 2e |
| ∛8 | |

> Note: There are 8 rational and 7 irrational numbers — match accordingly.

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Let me know if you'd like a printable version or explanation for any specific number!