Class 9th Mathematics - Number Systems

Number Systems - Class 9th Mathematics

Number systems form the foundation of mathematics. Understanding different types of numbers is crucial for higher mathematics.

Types of Numbers

• Natural Numbers (N): 1, 2, 3, 4, 5, ...
• Whole Numbers (W): 0, 1, 2, 3, 4, 5, ...
• Integers (Z): ..., -3, -2, -1, 0, 1, 2, 3, ...
• Rational Numbers (Q): Numbers that can be expressed as p/q where p and q are integers and q ≠ 0
• Irrational Numbers: Numbers that cannot be expressed as p/q (e.g., √2, π)
• Real Numbers (R): Combination of rational and irrational numbers

Properties of Rational Numbers

• Closure Property: Sum and product of rational numbers is rational
• Commutative Property: a + b = b + a and a × b = b × a
• Associative Property: (a + b) + c = a + (b + c)
• Distributive Property: a × (b + c) = a × b + a × c

Decimal Expansion

Every rational number has either a terminating decimal expansion or a non-terminating repeating decimal expansion.

Practice Problems

1. Express 0.375 as a rational number
2. Find three rational numbers between 1/3 and 1/2
3. Prove that √3 is irrational