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. 1.2̅ (repeating decimal: 1.222...)
- This is rational because it repeats.
- Can be written as a fraction: $ \frac{11}{9} $
- Not an integer, not whole, not 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 → perfect square
- So 9 is natural, whole, integer, rational, real

7. 3.456
- Terminating decimal → rational
- Not an integer → so only in Rational (not in integers or below)

8. –6/11
- Fraction → rational
- Negative → not whole or natural
- So: Rational, Real

9. –1.48298...
- The dots suggest non-repeating, non-terminating → Irrational
- But wait: Is it truly irrational? Let's see: if it's just a random-looking decimal with no pattern, assume it's irrational unless specified otherwise.
- So: Irrational, Real

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

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

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✔ Place each number in the Venn Diagram:

#### NATURAL:
→ 3, √81 (which is 9)

#### WHOLE:
→ 0, 3, √81 (9)

#### INTEGERS:
→ –19, 0, 3, –44, √81 (9)

#### RATIONAL (but not integer):
→ 1.2̅, 3.456, –6/11

#### IRRATIONAL:
→ √10, –1.48298..., π + 3

> Note: –1.48298... is assumed irrational due to non-repeating/non-terminating notation.

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Answer Key for Part 1 (Where to place):

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

Now place these in the diagram accordingly.

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2) List all classifications of the number.

a) √10
- √10 ≈ 3.162... → irrational, but real
✔ Irrational, Real

b) –44
- Negative integer → Integer, Rational, Real
✔ Integer, Rational, Real

c) 3
- Positive whole number → Natural, Whole, Integer, Rational, Real
✔ Natural, Whole, Integer, Rational, Real

d) –6/11
- Fraction → Rational, Real
- Not integer, not whole, not natural
✔ Rational, Real

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3) Check all boxes that apply to the number.

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

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✔ Final Answers:

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Part 1: Venn Diagram Placement

- Natural: 3, √81
- Whole: 0, 3, √81
- Integer: –19, 0, 3, –44, √81
- Rational (not integer): 1.2̅, 3.456, –6/11
- Irrational: √10, –1.48298..., π + 3

> Remember: All numbers listed are real numbers, so they go in the outer box.

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Part 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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Part 3: Checkboxes

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

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Let me know if you'd like a visual version of the Venn diagram filled out!