Number Set Worksheet-2 | PDF - Free Printable

Let's solve this Number Classification Worksheet step by step.

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1) Re-write each number in the Venn Diagram where it belongs.

We are given a list of numbers and need to classify them into the correct regions of the Venn diagram for real numbers:

- Real Numbers → split into:
- Rational (can be written as a fraction, terminating or repeating decimals)
- Irrational (non-repeating, non-terminating decimals, like √2, π)

Then within Rational, we have:
- Integers (positive and negative whole numbers, including zero)
- Within Integers: Whole numbers (0, 1, 2, 3, ...)
- Within Whole: Natural numbers (1, 2, 3, ...)

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#### Given Numbers:

1. –19
- Integer, Rational, Real
- Not whole or natural (negative)

2. 1.2̄ (repeating decimal = 1.222...)
- This is rational because it repeats.
- Can be written as a fraction: $ \frac{11}{9} $
- Not an integer, so not whole or natural

3. 0
- Whole, Integer, Rational, Real
- Not natural (natural numbers start at 1)

4. 3
- Natural, Whole, Integer, Rational, Real

5. √10
- √10 ≈ 3.162..., non-repeating, non-terminating → Irrational
- So only in Irrational and Real

6. √81
- √81 = 9 → whole number
- So: Natural, Whole, Integer, Rational, Real

7. 3.456
- Terminating decimal → Rational
- Not an integer → not whole or natural

8. –6/11
- Fraction → Rational
- Negative → not whole or natural

9. –1.48298... (with dots indicating non-repeating/non-terminating)
- If it’s truly non-repeating and non-terminating, it’s Irrational
- But if it’s just shown with ellipsis and no pattern, assume it's irrational unless stated otherwise.
- So: Irrational, Real

10. π + 3
- π is irrational; adding a rational (3) to irrational gives irrational
- So: Irrational, Real

11. –44
- Integer, Rational, Real
- Not whole or natural

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#### Now place them in the Venn Diagram:

```
REAL NUMBERS
├── RATIONAL
│ ├── INTEGERS
│ │ ├── WHOLE
│ │ │ └── NATURAL
│ │ │ ▶ 3
│ │ │ ▶ √81 (=9)
│ │ │
│ │ ▶ –19
│ │ ▶ –44
│ │
│ ▶ 1.2̄
│ ▶ 3.456
│ ▶ –6/11
│
└── IRRATIONAL
▶ √10
▶ –1.48298...
▶ π + 3
```

> Note: 0 goes in Whole, Integer, Rational, but not Natural.

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✔ Final Placement Summary:

| Number | Classification |
|---------------|----------------|
| –19 | Integer, Rational, Real |
| 1.2̄ | Rational, Real |
| 0 | Whole, Integer, Rational, Real |
| 3 | Natural, Whole, Integer, Rational, Real |
| √10 | Irrational, Real |
| √81 = 9 | Natural, Whole, Integer, Rational, Real |
| 3.456 | Rational, Real |
| –6/11 | Rational, Real |
| –1.48298... | Irrational, Real |
| π + 3 | Irrational, Real |
| –44 | Integer, Rational, Real |

Now fill in the diagram accordingly.

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2) List all classifications of the number.

a) √10
→ Irrational, Real
*(Not rational, not integer, etc.)*

b) –44
→ Integer, Rational, Real
*(Negative, so not whole or natural)*

c) 3
→ Natural, Whole, Integer, Rational, Real

d) –6/11
→ Rational, Real
*(Fraction, not integer, not whole, not natural)*

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3) Check all boxes that apply to the number.

| Number | Natural | Whole | Integer | Rational | Irrational | Real |
|------------|--------|-------|---------|----------|------------|------|
| a) √81 | ✔ | ✔ | ✔ | ✔ | ✘ | ✔ |
| b) 1.2̄ | ✘ | ✘ | ✘ | ✔ | ✘ | ✔ |
| c) 0 | ✘ | ✔ | ✔ | ✔ | ✘ | ✔ |
| d) 13 | ✔ | ✔ | ✔ | ✔ | ✘ | ✔ |

> Notes:
> - √81 = 9 → yes to all except irrational
> - 1.2̄ = 11/9 → rational, not integer
> - 0 is whole and integer, but not natural (some definitions include 0, but standard math curriculum says natural starts at 1)
> - 13 is positive whole number → natural, whole, integer, rational, real

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✔ Final Answers:

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#### 1) Venn Diagram Placement:

- NATURAL: 3, √81 (since √81 = 9)
- WHOLE: 0, 3, √81
- INTEGERS: –19, 0, 3, –44, √81
- RATIONAL (but not integer): 1.2̄, 3.456, –6/11
- IRRATIONAL: √10, –1.48298..., π + 3

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#### 2) Classifications:

a) √10 → Irrational, Real
b) –44 → Integer, Rational, Real
c) 3 → Natural, Whole, Integer, Rational, Real
d) –6/11 → Rational, Real

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#### 3) Checkboxes:

| Number | Natural | Whole | Integer | Rational | Irrational | Real |
|------------|--------|-------|---------|----------|------------|------|
| a) √81 | ✔ | ✔ | ✔ | ✔ | ✘ | ✔ |
| b) 1.2̄ | ✘ | ✘ | ✘ | ✔ | ✘ | ✔ |
| c) 0 | ✘ | ✔ | ✔ | ✔ | ✘ | ✔ |
| d) 13 | ✔ | ✔ | ✔ | ✔ | ✘ | ✔ |

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✔ All done! Let me know if you'd like this formatted as a printable answer sheet.