Exercise 1.1 of Real Numbers is part of the latest Class 9 Mathematics syllabus in Pakistan (Punjab, Federal, and other boards). This exercise introduces the basics of rational and irrational numbers, their representation on the number line, and the fundamental properties of real numbers. These concepts form the foundation for higher mathematics.
Real Numbers – Exercise 1.1
Key Topics in Exercise 1.1
- Difference between rational and irrational numbers with examples.
- Plotting numbers like √2, √3, etc. on the number line.
- Converting recurring decimals (e.g., 0.333…, 0.1212…) into fractions.
- Understanding the properties of real numbers: commutative, associative, distributive, and identity.
Why These Notes Are Helpful
- Helps students solve common exam questions confidently.
- Builds strong conceptual clarity for advanced chapters.
- Step-by-step solutions make even tricky number line questions easy.
- Recurring decimal conversion practice improves speed and accuracy.
Study Tips
- Memorize the definitions of rational and irrational numbers with simple examples.
- Practice plotting square roots carefully on the number line.
- Revise recurring decimal conversions multiple times to avoid mistakes.
- Use solved examples to understand the properties of real numbers clearly.