← GSEB Class 9
Number Systems
Chapter Overview
Number systems form the foundation of mathematics. Natural numbers (N = {1,2,3,...}), whole numbers (W = {0,1,2,...}), integers (Z = {...,-2,-1,0,1,2,...}), rational numbers (p/q where q != 0), and irrational numbers (non-terminating non-repeating decimals) are covered. Real numbers include both rational and irrational numbers. The chapter covers locating irrational numbers on the number line, operations on real numbers, rationalization of denominators, and laws of exponents for real numbers.
Topics Covered
- Natural Numbers
- Whole Numbers
- Integers
- Rational Numbers
- Irrational Numbers
- Real Numbers
- Number Line Representation
- Rationalization
- Laws of Exponents
Key Formulas
√a x √b = √ab
√a/√b = √a/b
(√a + √b)(√a - √b) = a - b
am x an = am+n
(am)n = amn
Real-World Applications
Applications: Digital computing (binary systems), cryptography, measurement and precision in engineering.
Study Tips
Tip: Understand the difference between rational and irrational numbers
Tip: Practice rationalization techniques
Tip: Learn the laws of exponents for real numbers