Number Classification Worksheet with Venn diagram and classification exercises.

Let’s solve each part step by step.

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

We have these numbers:
- -19
- 1.2̅ (which means 1.222... repeating)
- 0
- 3
- √10
- √81
- 3.456
- -6/11
- -1.48298..... (non-repeating, non-terminating decimal — likely irrational)
- π + 3 (π is irrational, so adding 3 keeps it irrational)
- -44

First, let’s recall what each set means:

- Natural Numbers: Counting numbers starting from 1 → {1, 2, 3, ...}
- Whole Numbers: Natural numbers plus zero → {0, 1, 2, 3, ...}
- Integers: Whole numbers and their negatives → {..., -3, -2, -1, 0, 1, 2, 3, ...}
- Rational Numbers: Any number that can be written as a fraction of two integers (including terminating or repeating decimals).
- Irrational Numbers: Cannot be written as a fraction; non-repeating, non-terminating decimals (like √2, π).
- Real Numbers: All rational and irrational numbers together.

Now classify each number:

1. -19 → Integer, Rational, Real
(It’s negative whole number → integer → rational)

2. 1.2̅ → Rational, Real
(Repeating decimal = rational)

3. 0 → Whole, Integer, Rational, Real
(Zero is whole, not natural)

4. 3 → Natural, Whole, Integer, Rational, Real
(Positive counting number)

5. √10 → Irrational, Real
(√10 ≈ 3.162..., doesn’t simplify to whole number → irrational)

6. √81 → Natural, Whole, Integer, Rational, Real
(√81 = 9 → which is natural)

7. 3.456 → Rational, Real
(Terminating decimal → rational)

8. -6/11 → Rational, Real
(Fraction → rational)

9. -1.48298..... → Irrational, Real
(Assuming this is non-repeating, non-terminating → irrational)

10. π + 3 → Irrational, Real
(π is irrational, adding rational doesn’t make it rational)

11. -44 → Integer, Rational, Real
(Negative whole number → integer → rational)

Now place them in the Venn diagram sections:

- Natural: 3, √81 (since √81=9)
- Whole: 0, 3, √81
- Integer: -19, 0, 3, √81, -44
- Rational: -19, 1.2̅, 0, 3, √81, 3.456, -6/11, -44
- Irrational: √10, -1.48298....., π + 3
- Real: ALL of them (since all are real numbers)

Note: The Venn diagram has nested boxes inside “Rational” for Integers → Whole → Natural. So we put numbers in the innermost box they belong to.

So final placement:

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

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Part 2: List all classifications of the number.

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

(Note: We don’t list “Real” every time if the question implies only specific categories, but since it says “all classifications”, and Real includes everything, we include it.)

But looking at context, probably they want the most specific ones. Let’s check standard practice: usually, you list all sets it belongs to, including Real.

However, sometimes teachers expect only the most specific ones. But since Part 3 asks to check boxes including Real, we’ll include Real here too.

Actually, let’s look again: In Part 2, it says “List all classifications”. Since Real is always true for any number on this sheet, maybe they mean the sub-classifications. But to be safe, I’ll include Real.

Wait — in many curricula, when they say “classifications”, they mean Natural, Whole, Integer, Rational, Irrational — and Real is assumed. But since Real is listed separately in Part 3, perhaps here they want all applicable.

To avoid confusion, let’s follow the structure of Part 3: Natural, Whole, Integer, Rational, Irrational, Real.

So:

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

Yes.

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Part 3: Check all boxes that apply to the number.

We have a table with columns: Natural, Whole, Integer, Rational, Irrational, Real

Rows:

a) √81 → which is 9 → so: Natural, Whole, Integer, Rational, Real → NOT Irrational

b) 1.2̅ → repeating decimal → Rational, Real → NOT Natural, Whole, Integer, Irrational

c) 0 → Whole, Integer, Rational, Real → NOT Natural, NOT Irrational

d) 13 → Natural, Whole, Integer, Rational, Real → NOT Irrational

Let’s fill the table:

For a) √81 = 9:
- Natural: ✓
- Whole: ✓
- Integer: ✓
- Rational: ✓
- Irrational: ✗
- Real: ✓

For b) 1.2̅:
- Natural: ✗
- Whole: ✗
- Integer: ✗
- Rational: ✓
- Irrational: ✗
- Real: ✓

For c) 0:
- Natural: ✗
- Whole: ✓
- Integer: ✓
- Rational: ✓
- Irrational: ✗
- Real: ✓

For d) 13:
- Natural: ✓
- Whole: ✓
- Integer: ✓
- Rational: ✓
- Irrational: ✗
- Real: ✓

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Now, compiling final answers.

Final Answer:

Part 1: Venn Diagram Placement

- Natural: 3, √81
- Whole (only): 0
- Integer (only): -19, -44
- Rational (only): 1.2̅, 3.456, -6/11
- Irrational: √10, -1.48298....., π + 3

*(Note: All numbers go under Real, but since Real is the outermost, we don't list them again.)*

Part 2: Classifications

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

Part 3: Table Checks

a) √81: Natural ✓, Whole ✓, Integer ✓, Rational ✓, Irrational ✗, Real ✓
b) 1.2̅: Natural ✗, Whole ✗, Integer ✗, Rational ✓, Irrational ✗, Real ✓
c) 0: Natural ✗, Whole ✓, Integer ✓, Rational ✓, Irrational ✗, Real ✓
d) 13: Natural ✓, Whole ✓, Integer ✓, Rational ✓, Irrational ✗, Real ✓