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Number System — Syllabus

Gujarat Board · Class 9 · Mathematics

What Number System covers in Gujarat Board Class 9 Mathematics: 4 topics, for the 2026-27 session. Part of the Gujarat Board Class 9 Mathematics syllabus.

45 questions28 flashcards5 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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4 Topics · Gujarat Board Class 9 Mathematics · 2026-27

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

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Frequently Asked Questions

What are the important topics in Number System for Gujarat Board Class 9 Mathematics?
Key topics in Number System include Types of Numbers – The Complete Picture, Irrational Numbers and Their Properties, Decimal Expansions of Real Numbers, Operations on Real 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 45 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 Gujarat Board Class 9 Mathematics Syllabus

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