Educational worksheet for classifying rational and irrational numbers.

Let’s go through each number one by one and decide whether it is rational or irrational.

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What do we mean?

- A rational number can be written as a fraction (like 1/2, 3/4, etc.) — even if it looks like a decimal, if it ends or repeats, it’s rational.
- An irrational number cannot be written as a simple fraction. Its decimal goes on forever without repeating. Examples: π, e, √2, ∛9.

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Now let’s check each number:

#### Row 1:
1. 3.14 → This is a terminating decimal → Rational
2. 0.444 → Terminating decimal → Rational
3. √121 → √121 = 11 → whole number → Rational
4. √1000 → Not a perfect square → √1000 ≈ 31.62... and doesn’t repeat → Irrational
5. π → Famous irrational number → Irrational

#### Row 2:
6. π/7 → π is irrational, dividing by 7 still leaves it irrational → Irrational
7. 0.333... → Repeating decimal = 1/3 → Rational
8. 1.12313... → The “...” with no pattern shown means it’s non-repeating → Irrational
- *Note: If this were meant to be repeating, it would have bars or dots over repeating digits. Since it says “...” and no pattern, we assume irrational.*
9. 0.1̅2̅ → The bar means 0.121212... → repeating → Rational
10. e → Euler’s number, famous irrational → Irrational

#### Row 3:
11. ∛9 → Cube root of 9 is not a whole number, and doesn’t terminate or repeat → Irrational
12. 2.9̅ → That’s 2.9999... which equals 3 → Rational
- *Fun fact: 0.999... = 1, so 2.999... = 3*
13. 2e → e is irrational, multiplying by 2 keeps it irrational → Irrational
14. 1.2̅3̅4̅ → Repeating decimal → Rational
15. ∛8 → Cube root of 8 = 2 → whole number → Rational

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Now sort them:

#### Rational Numbers:
- 3.14
- 0.444
- √121 (=11)
- 0.333...
- 0.1̅2̅
- 2.9̅ (=3)
- 1.2̅34̅
- ∛8 (=2)

→ That’s 8 rational numbers

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

→ That’s 7 irrational numbers

Wait — let’s count again from the list:

Total items: 15

We listed 8 rational + 7 irrational = 15 ✔️

But looking at the worksheet layout:

The “Rational” column has 8 boxes, and “Irrational” has 7 boxes — matches perfectly!

So final sorting:

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✔ Rational:
- 3.14
- 0.444
- √121
- 0.333...
- 0.1̅2̅
- 2.9̅
- 1.2̅34̅
- ∛8

✔ Irrational:
- √1000
- π
- π/7
- 1.12313...
- e
- ∛9
- 2e

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Final Answer:
Rational: 3.14, 0.444, √121, 0.333..., 0.1̅2̅, 2.9̅, 1.2̅3̅4, ∛8
Irrational: √1000, π, π/7, 1.12313..., e, ∛9, 2e