In ICSE Class 9 Mathematics, the topic of rational and irrational numbers is essential. Here’s a summary of this topic:

1. **Rational Numbers**: Rational numbers are numbers that can be expressed as a fraction p/q, where p and q are integers and q is not equal to 0. They can be finite decimals (like 0.25) or recurring decimals (like 0.333…).

2. **Irrational Numbers**: Irrational numbers are numbers that cannot be expressed as a fraction of two integers. They have non-terminating and non-repeating decimal expansions. Examples include √2, √3, and π.

3. **Real Numbers**: Real numbers include both rational and irrational numbers. They are located on the number line, with rational numbers being represented as points with finite or repeating decimals, and irrational numbers being represented as points with non-repeating, non-terminating decimals.

4. **Operations with Rational and Irrational Numbers**:

– Addition and subtraction: Rational and irrational numbers can be added or subtracted like terms.

– Multiplication: When multiplying a rational number by an irrational number, the result is irrational.

– Division: Division of a rational number by an irrational number can result in either a rational or an irrational number, depending on the numbers involved.

5. **Properties of Irrational Numbers**:

– They are non-repeating and non-terminating.

– They cannot be expressed as a simple fraction.

– They are dense on the number line, meaning between any two rational numbers, there exists an irrational number.

Understanding rational and irrational numbers is fundamental in mathematics, as they form the basis for various mathematical concepts and calculations.