Number System
Uttar Pradesh Board · Class 9 · Mathematics
Quick revision notes for Number System — Uttar Pradesh Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
Key Topics to Revise
Types of Numbers
- Natural Numbers (N): 1, 2, 3, 4, ... (counting numbers)
- Whole Numbers (W): 0, 1, 2, 3, 4, ... (natural numbers including zero)
- Integers (Z): ..., -3, -2, -1, 0, 1, 2, 3, ... (positive and negative whole numbers)
Decimal Representations
- Terminating decimals: Decimal expansion ends after finite digits (e.g., 0.25, 0.375)
- Non-terminating recurring decimals: Decimal expansion continues indefinitely with repeating pattern (e.g., 0.333..., 1.272727...)
- Non-terminating non-recurring decimals: Decimal expansion continues indefinitely without repeating pattern (irrational numbers)
Representation on Number Line
- Every real number can be represented as a point on the number line
- Square roots of non-perfect squares are irrational and can be located using geometric construction
- Pythagoras theorem is used to construct square roots on number line
Finding Rational and Irrational Numbers
- Between any two rational numbers, there exist infinitely many rational numbers
- Between any two rational numbers, there exist infinitely many irrational numbers
- Method 1 for finding rational numbers: Use (a+b)/2 repeatedly
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Number System covers several key topics that are frequently asked in Uttar Pradesh 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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