Solved Name: Period: Number Classification Worksheet 1) | Chegg.com - 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 place them in the correct region of the Venn diagram for real numbers, which includes:

- Real Numbers
- Rational
- Integers
- Whole
- Natural
- Irrational

Let’s classify each number:

#### Given numbers:
1. $-19$
2. $1.\overline{2}$ (repeating decimal)
3. $0$
4. $3$
5. $\sqrt{10}$
6. $\sqrt{81}$
7. $3.456$
8. $-\frac{4}{11}$
9. $-1.48298...$ (non-repeating, non-terminating — likely irrational)
10. $\pi + 3$
11. $-44$

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Now classify each:

| Number | Classification | Reason |
|--------|----------------|--------|
| $-19$ | Integer, Rational, Real | Negative whole number |
| $1.\overline{2}$ | Rational, Real | Repeating decimal = fraction |
| $0$ | Whole, Integer, Rational, Real | Zero is included in all except Natural |
| $3$ | Natural, Whole, Integer, Rational, Real | Positive integer |
| $\sqrt{10}$ | Irrational, Real | √10 ≈ 3.16..., not perfect square |
| $\sqrt{81}$ | $= 9$ → Natural, Whole, Integer, Rational, Real | √81 = 9 |
| $3.456$ | Rational, Real | Terminating decimal |
| $-\frac{4}{11}$ | Rational, Real | Fraction |
| $-1.48298...$ | Irrational, Real | Non-repeating, non-terminating decimal |
| $\pi + 3$ | Irrational, Real | π is irrational; adding rational doesn't make it rational |
| $-44$ | Integer, Rational, Real | Negative integer |

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Venn Diagram Placement:

- Natural: $3$, $\sqrt{81} = 9$
- Whole: $0$, $3$, $\sqrt{81} = 9$
- Integer: $-19$, $0$, $3$, $-44$, $\sqrt{81} = 9$
- Rational: $-19$, $1.\overline{2}$, $0$, $3$, $3.456$, $-\frac{4}{11}$, $-44$, $\sqrt{81} = 9$
- Irrational: $\sqrt{10}$, $-1.48298...$, $\pi + 3$
- Real: All of the above

> So place each number in the appropriate box based on the hierarchy.

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2) List all classifications of the number.

#### a) $\sqrt{10}$

- Irrational, Real

> Because √10 is not a perfect square and cannot be expressed as a fraction.

#### b) $-44$

- Integer, Rational, Real

> It's a negative whole number.

#### c) $3$

- Natural, Whole, Integer, Rational, Real

> Positive whole number.

#### d) $-\frac{4}{11}$

- Rational, Real

> It's a fraction (ratio of integers), so rational.

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3) Check all boxes that apply to the number.

| Number | Natural | Whole | Integer | Rational | Irrational | Real |
|--------|---------|-------|---------|----------|------------|------|
| a) $\sqrt{81}$ | ✔ | ✔ | ✔ | ✔ | ✘ | ✔ |
| b) $1.\overline{2}$ | ✘ | ✘ | ✘ | ✔ | ✘ | ✔ |
| c) $0$ | ✘ | ✔ | ✔ | ✔ | ✘ | ✔ |
| d) $13$ | ✔ | ✔ | ✔ | ✔ | ✘ | ✔ |

> Explanation:
- $\sqrt{81} = 9$: natural, whole, integer, rational, real
- $1.\overline{2}$: repeating decimal → rational, real
- $0$: whole, integer, rational, real (not natural — some definitions include 0, but standardly natural numbers start at 1)
- $13$: natural, whole, integer, rational, real

> Note: Natural numbers usually refer to positive integers starting from 1 (i.e., 1, 2, 3, ...). So 0 is not natural.

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✔ Final Answers:

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1) Venn Diagram Placement:

- Natural: $3$, $\sqrt{81}$
- Whole: $0$, $3$, $\sqrt{81}$
- Integer: $-19$, $0$, $3$, $-44$, $\sqrt{81}$
- Rational: $-19$, $1.\overline{2}$, $0$, $3$, $3.456$, $-\frac{4}{11}$, $-44$, $\sqrt{81}$
- Irrational: $\sqrt{10}$, $-1.48298...$, $\pi + 3$
- Real: All numbers

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2) Classifications:

a) $\sqrt{10}$ → Irrational, Real
b) $-44$ → Integer, Rational, Real
c) $3$ → Natural, Whole, Integer, Rational, Real
d) $-\frac{4}{11}$ → Rational, Real

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3) Checkboxes:

| Number | Natural | Whole | Integer | Rational | Irrational | Real |
|--------|---------|-------|---------|----------|------------|------|
| a) $\sqrt{81}$ | ✔ | ✔ | ✔ | ✔ | ✘ | ✔ |
| b) $1.\overline{2}$ | ✘ | ✘ | ✘ | ✔ | ✘ | ✔ |
| c) $0$ | ✘ | ✔ | ✔ | ✔ | ✘ | ✔ |
| d) $13$ | ✔ | ✔ | ✔ | ✔ | ✘ | ✔ |

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