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Number System

Gujarat Board · Class 9 · Mathematics

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

45 questions24 flashcards5 concepts

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Key Topics to Revise

1

Types of Numbers and Their Relationships

  • Natural numbers (N): 1, 2, 3, 4, ... - counting numbers used in daily life
  • Whole numbers (W): 0, 1, 2, 3, ... - natural numbers including zero
  • Integers (Z): ..., -3, -2, -1, 0, 1, 2, 3, ... - whole numbers including negatives
2

Irrational Numbers and Number Line Representation

  • Examples of irrational numbers: √2, √3, √5, π, 0.101100111000111...
  • √2 was the first irrational number discovered by Pythagoreans around 400 BC
  • Irrational numbers have non-terminating, non-recurring decimal expansions
3

Decimal Expansions of Real Numbers

  • Rational numbers have either terminating or non-terminating recurring decimal expansions
  • Terminating decimals: remainder becomes zero (e.g., 7/8 = 0.875)
  • Non-terminating recurring: remainder repeats (e.g., 1/3 = 0.3̄, 1/7 = 0.142857̄)
4

Operations on Real Numbers

  • Sum/difference of rational and irrational is always irrational
  • Product/quotient of non-zero rational and irrational is always irrational
  • Sum/difference/product/quotient of two irrationals may be rational or irrational

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Full Notes

Key Concepts

Numbers are organized into hierarchical setsA rational number can be writtenNumbers that cannot be expressed asRational numbers have either terminating decimalsThe collection of all rational

Frequently Asked Questions

What are the important topics in Number System for Gujarat Board Class 9 Mathematics?
Number System covers several key topics that are frequently asked in Gujarat Board Class 9 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Number System — Gujarat Board Class 9 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision 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 12 chapters — Gujarat Board Class 9 Mathematics Revision Notes

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