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Number System — Revision Notes

Madhya Pradesh Board · Class 9 · Mathematics

Number System revision notes for Madhya Pradesh Board Class 9 Mathematics: 4 topics in quick points. Includes Types of Numbers, Decimal Representations.

29 questions25 flashcards3 formulas & key relations5 concepts

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A nested Venn diagram illustrating the relationships between natural numbers (N), integers (Z), rational numbers (Q), and real numbers (R) as subsets of each other.
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Key Topics to Revise

1

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)
2

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)
3

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
4

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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Full Notes

Key Concepts

Natural numbers (1Every integer is a rational numberNumbers like √2Using Pythagoras theorem and compass constructionTerminating decimals (finite digits after decimal

Frequently Asked Questions

What are the important topics in Number System for Madhya Pradesh Board Class 9 Mathematics?
Key topics in Number System include Types of Numbers, Decimal Representations, Representation on Number Line, Finding Rational and Irrational Numbers. Study these first, then practise questions on each for Class 9 exams.
How should I revise Number System for Class 9 exams?
Learn the core ideas first, then work through the 29 practice questions on Number System. 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 Madhya Pradesh Board Class 9 Mathematics Revision Notes

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