Real Numbers
Maharashtra Board · Class 9 · Mathematics
Quick revision notes for Real Numbers — Maharashtra Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Number Systems and Their Properties
- Natural numbers N = {1, 2, 3, 4, ...} are counting numbers
- Whole numbers W = {0, 1, 2, 3, 4, ...} include zero with natural numbers
- Integers I = {..., -3, -2, -1, 0, 1, 2, 3, ...} include positive and negative whole numbers
Properties of Rational Numbers
- Commutative property holds for both addition and multiplication
- Associative property applies to addition and multiplication
- Identity elements: 0 for addition, 1 for multiplication
Irrational Numbers
- Numbers that cannot be expressed as p/q where p, q are integers
- Decimal expansion is non-terminating and non-recurring
- √2, √3, √5, π are common examples
Surds and Their Operations
- A surd is an irrational root of a positive rational number
- Quadratic surds have order 2 (like √3, √7)
- Surds can be simplified by factoring perfect squares
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Real Numbers covers several key topics that are frequently asked in Maharashtra Board Class 9 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
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