CBSE Class 7 Maths Rational Numbers Worksheet | Class1to12.com - Free Printable

The image you've uploaded is a mathematics lesson page from a Grade 7 textbook, focusing on Unit 12 – Rational Numbers. It explains the types of numbers, their relationships, and definitions with examples.

There is no specific problem or question directly stated in the image — it's an explanatory page designed to teach concepts about rational and irrational numbers.

However, I can analyze and explain the content thoroughly so that you understand it well, and if needed, we can create or solve related problems based on this material.

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🔍 Explanation of the Content

#### 🟦 1. Venn Diagram: Types of Numbers
The diagram shows how different sets of numbers are related:

- Natural Numbers: Counting numbers starting from 1 → {1, 2, 3, 4, ...}
- Whole Numbers: Natural numbers + 0 → {0, 1, 2, 3, ...}
- Integers: Whole numbers + negative numbers → {..., -3, -2, -1, 0, 1, 2, 3, ...}
- Rational Numbers: Any number that can be written as a fraction (ratio) of two integers, where the denominator ≠ 0.
- Includes terminating decimals (e.g., 0.5), repeating decimals (e.g., 0.333...), and fractions.
- Irrational Numbers: Numbers that cannot be expressed as a ratio of two integers.
- Examples: √2, π, √72, √(8/23)
- Their decimal representations are non-repeating and non-terminating.

> Note: The Real Numbers set includes both rational and irrational numbers.

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✔ Definitions Recap

| Term | Definition |
|------|-----------|
| Real Numbers | All rational and irrational numbers combined. |
| Natural Numbers | Positive integers starting from 1: 1, 2, 3, ... |
| Whole Numbers | Natural numbers plus zero: 0, 1, 2, 3, ... |
| Integers | Whole numbers and their negatives: ..., -2, -1, 0, 1, 2, ... |
| Rational Number | A number that can be written as $ \frac{p}{q} $, where $ p $ and $ q $ are integers and $ q \ne 0 $. Includes fractions, terminating decimals, and repeating decimals. |

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📌 Examples Given

#### Rational Numbers:
- $ \frac{3}{5} $ → fraction of integers
- $ \frac{9}{4} $ → fraction of integers
- $ 8 = \frac{8}{1} $ → any integer is rational
- $ 0.25 = \frac{1}{4} = \frac{25}{100} $ → terminating decimal

#### Irrational Numbers:
- $ \sqrt{2} $ → cannot be written as a simple fraction; non-repeating, non-terminating
- $ \pi $ → known constant, approximately 3.14159..., never repeats
- $ \sqrt{72} $ → simplifies to $ 6\sqrt{2} $, still irrational
- $ \sqrt{\frac{8}{23}} $ → irrational because it’s not a perfect square

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🔄 Key Concept: Rational vs Irrational

| Feature | Rational Numbers | Irrational Numbers |
|--------|------------------|--------------------|
| Can be written as a fraction? | ✔ Yes | ✘ No |
| Decimal form | Terminates or repeats | Never terminates or repeats |
| Examples | ½, 0.75, 0.333..., 4 | √3, π, e, √5 |

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💡 Example Problem Based on This Page

Let’s say the task was:
> Classify the following numbers: 0.666..., √16, -7, π, 3.14, ½

We would solve it like this:

1. 0.666... → Repeating decimal → Rational
(Can be written as $ \frac{2}{3} $)

2. √16 → $ \sqrt{16} = 4 $ → Integer → Rational

3. -7 → Integer → Rational

4. π → Non-repeating, non-terminating → Irrational

5. 3.14 → Terminating decimal → Rational
(Even though it looks like π, 3.14 is just an approximation)

6. ½ → Fraction → Rational

✔ Final Answer:
- Rational: 0.666..., √16, -7, 3.14, ½
- Irrational: π

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✔ Summary

This page teaches students how to:
- Understand the hierarchy of number sets.
- Distinguish between rational and irrational numbers.
- Recognize that all integers, fractions, and terminating/repeating decimals are rational.
- Identify common irrational numbers like √2 and π.

If you have a specific question or problem related to this topic (e.g., classify a number, convert a decimal to a fraction, etc.), please share it, and I’ll help you solve it step by step!