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Number Systems — Revision Notes

Karnataka Board · Class 9 · Mathematics

Number Systems revision notes for Karnataka Board Class 9 Mathematics: 4 topics in quick points. Part of the Karnataka Board Class 9 Mathematics syllabus.

28 questions20 flashcards2 formulas & key relations5 concepts

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Key Topics to Revise

1

1. Classification of Numbers

  • Natural Numbers (N): 1, 2, 3, 4, ... (counting numbers)
  • Whole Numbers (W): 0, 1, 2, 3, 4, ... (natural numbers + zero)
  • Integers (Z): ..., -3, -2, -1, 0, 1, 2, 3, ... (positive and negative whole numbers)
2

2. Finding Rational Numbers Between Given Numbers

  • There are infinitely many rational numbers between any two rational numbers
  • Method 1: Average method - find (a+b)/2 between numbers a and b
  • Method 2: Equivalent fraction method - express both numbers with same denominator
3

3. Representation of Numbers on Number Line

  • Every real number corresponds to a unique point on the number line
  • Use Pythagoras theorem to locate square roots on number line
  • Construct right triangles with appropriate sides to find √n
4

4. Decimal Expansions of Rational Numbers

  • Rational numbers have either terminating or non-terminating recurring decimal expansions
  • Terminating: decimal expansion ends after finite digits (like 0.5, 0.75)
  • Non-terminating recurring: decimal expansion repeats a block of digits (like 0.333...)

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Full Notes

Key Concepts

Numbers are classified intoA rational number can be writtenNumbers that cannot be expressed asThree typesKey rules

Frequently Asked Questions

What are the important topics in Number Systems for Karnataka Board Class 9 Mathematics?
Key topics in Number Systems include Classification of Numbers, Finding Rational Numbers Between Given Numbers, Representation of Numbers on Number Line, Decimal Expansions of Rational Numbers. Study these first, then practise questions on each for Class 9 exams.
How should I revise Number Systems for Class 9 exams?
Learn the core ideas first, then work through the 28 practice questions on Number Systems. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All Karnataka Board Class 9 Mathematics Revision Notes

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