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Revision Notes
Number System — Revision Notes
Gujarat Board · Class 9 · Mathematics
Number System revision notes for Gujarat Board Class 9 Mathematics: 4 topics in quick points. Part of the Gujarat Board Class 9 Mathematics syllabus.
45 questions28 flashcards5 formulas & key relations5 concepts
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Key Topics to Revise
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
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Full NotesKey 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 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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