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Number System

Gujarat Board · Class 9 · Mathematics

Complete topic list for Number System in Gujarat Board Class 9 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

45 questions28 flashcards5 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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4 Topics · Gujarat Board Class 9 Mathematics

Topics in Number System

1

Types of Numbers – The Complete Picture

  • Natural Numbers (N): 1, 2, 3, 4, ... — counting numbers, starting from 1
  • Whole Numbers (W): 0, 1, 2, 3, ... — natural numbers plus zero
  • Integers (Z): ..., -3, -2, -1, 0, 1, 2, 3, ... — includes negative numbers, zero, and positive numbers
2

Irrational Numbers and Their Properties

  • Irrational numbers were first discovered by the Pythagoreans around 400 BC
  • √2 was the first irrational number proved to be irrational
  • Examples of irrational numbers: √2, √3, √5, √7, π, 0.10110111011110...
3

Decimal Expansions of Real Numbers

  • Every rational number has a decimal expansion that is either TERMINATING or NON-TERMINATING RECURRING
  • Every irrational number has a decimal expansion that is NON-TERMINATING NON-RECURRING
  • Terminating decimal: remainder becomes zero after some steps. Example: 7/8 = 0.875
4

Operations on Real Numbers

  • Rational + Rational = Always Rational
  • Irrational + Irrational = Can be rational OR irrational. Example: √2 + (-√2) = 0 (rational); √2 + √3 (irrational)
  • Rational + Irrational = Always Irrational. Example: 2 + √3 is always irrational

Key Concepts

The set of counting numbers startingThe set of natural numbers plusThe set of all whole numbersA number 'p' is rational ifA number 's' is irrational if

Frequently Asked Questions

What are the important topics in Number System for Gujarat Board Class 9 Mathematics?
Key topics in Number System include Number System Overview, Mind map showing the hierarchical classification of real numbers and how each type relates to others, Flowchart showing the decision process to determine if a number is rational. These are the concepts Gujarat Board Class 9 examiners draw on most — study them first, then practise related questions.
How to score full marks in Number System — Gujarat Board Class 9 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and 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.

More resources for Number System

All 12 chapters — Gujarat Board Class 9 Mathematics Syllabus

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