Exemplar L-03, Ch-1st, Examples and Ex 1.3 Questions 1-3

📒 Exemplar Problems of Class 9th maths
📘 Class 9 Maths Chapter 1 – Number Systems | Full Chapter Summary

In this chapter, "Number Systems", we explore the complete journey of numbers — from natural numbers to real numbers. It's the foundation of all mathematical learning. Here's what you'll learn in this chapter:

🔹 1. Review of Number Types

Natural Numbers (ℕ): 1, 2, 3, …

Whole Numbers (𝕎): 0, 1, 2, 3, …

Integers (ℤ): ..., -3, -2, -1, 0, 1, 2, 3, …

Rational Numbers (ℚ): Numbers that can be written in the form p/q, where p and q are integers and q ≠ 0.

Irrational Numbers: Numbers that cannot be written as p/q and have non-terminating, non-repeating decimal expansions, like √2, π.

🔹 2. Real Numbers (ℝ)

Combination of all rational and irrational numbers.

Real numbers can be represented on the number line.

🔹 3. Representation on the Number Line

Learn how to place irrational numbers like √2 and √3 on the number line using the Pythagoras Theorem.

🔹 4. Operations on Real Numbers

Addition, subtraction, multiplication, and division of rational and irrational numbers.

🔹 5. Laws of Exponents for Real Numbers

Important rules such as:
aᵐ × aⁿ = aᵐ⁺ⁿ
(aᵐ)ⁿ = aᵐⁿ
a⁰ = 1 (a ≠ 0), etc.

🔹 6. Rationalizing the Denominator

Method to simplify expressions like 1/√2 or 3/(2 + √3) to remove irrational numbers from the denominator.

🔹 7. Decimal Expansions

Rational numbers have either terminating or non-terminating but repeating decimals.

Irrational numbers have non-terminating, non-repeating decimals.

🔍 Key Concepts Covered:

Difference between rational and irrational numbers

How real numbers are formed

Visual representation of real numbers

Rules of exponents and simplification

Decimal classification of numbers

🎯 This chapter strengthens your base for future topics like algebra, geometry, and real-life math problems.


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