Skip to main content
Super TutorResources
Chapter 1 of 5
QuestionsNotesFlashcardsSummaryFormulasQuizConceptsSyllabusPlan
Revision Notes

Number System

Punjab Board · Class 9 · Mathematics

Quick revision notes for Number System — Punjab Board Class 9 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

43 questions28 flashcards5 concepts

Interactive on Super Tutor

Studying Number System? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for revision notes and more.

Try Super Tutor — Free

1,000+ Class 9 students started this chapter today

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.
Super Tutor

Learn better with visuals Super Tutor has hundreds of illustrations like this across every chapter — all free to try.

Get started

Key Topics to Revise

1

Types of Numbers and Their Hierarchy

  • Natural Numbers (N): Counting numbers starting from 1. N = {1, 2, 3, 4, ...}. This set is infinite.
  • Whole Numbers (W): Natural numbers plus zero. W = {0, 1, 2, 3, ...}. Every natural number is a whole number, but 0 is NOT a natural number.
  • Integers (Z): All positive and negative whole numbers including zero. Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}. Every whole number is an integer.
2

Irrational Numbers and Locating Them on the Number Line

  • Irrational numbers were first discovered by the Pythagoreans around 400 BC. Hippacus of Croton discovered that √2 is irrational.
  • Examples of irrational numbers: √2, √3, √5, √7, √15, π, 0.10110111011110...
  • √4 = 2 (rational), √9 = 3 (rational) — perfect square roots are rational, non-perfect square roots are irrational.
3

Decimal Expansions of Real Numbers

  • TERMINATING DECIMAL: The decimal expansion ends (remainder becomes 0). Example: 7/8 = 0.875
  • NON-TERMINATING RECURRING (REPEATING): The decimal goes on forever but a block of digits repeats. Example: 1/7 = 0.142857142857... = 0.̄1̄4̄2̄8̄5̄7̄
  • NON-TERMINATING NON-RECURRING: The decimal goes on forever and NO block of digits repeats. Example: √2 = 1.4142135..., π = 3.14159...
4

Operations on Real Numbers and Rationalisation

  • Rational + Irrational = Irrational (e.g., 2 + √3 is irrational)
  • Rational × Irrational (non-zero) = Irrational (e.g., 2√3 is irrational)
  • Irrational ± Irrational = May be Rational or Irrational (e.g., √6 + (-√6) = 0, which is rational; but √2 + √3 is irrational)

Get complete notes with diagrams and examples

Full Notes

Key Concepts

Natural numbers are the counting numbersWhole numbers are natural numbers plusIntegers are whole numbers and theirA rational number is any numberAn irrational number is a number

Frequently Asked Questions

What are the important topics in Number System for Punjab Board Class 9 Mathematics?
Key topics in Number System include Real Number System Classification, Number System Classification and Relationships, A mind map showing the hierarchical classification of the real number system, illustrating how each category is nested within the larger categories. These are the concepts Punjab Board Class 9 examiners draw on most — study them first, then practise related questions.
How to score full marks in Number System — Punjab Board Class 9 Mathematics?
Understand the core concepts first, then work through the 43 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 5 chapters — Punjab Board Class 9 Mathematics Revision Notes

For serious students

Get the full Number System chapter — for free.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for Punjab Board Class 9 Mathematics.

Try Super Tutor Free
Try the full chapter — Free