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Number System — Revision Notes

Punjab Board · Class 9 · Mathematics

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

43 questions28 flashcards10 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 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)

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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 Types of Numbers and Their Hierarchy, Irrational Numbers and Locating Them on the Number Line, Decimal Expansions of Real Numbers, Operations on Real Numbers and Rationalisation. 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 43 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 Punjab Board Class 9 Mathematics Revision Notes

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