Chapter 3 of 16
Revision Notes
Real Numbers — Revision Notes
Maharashtra Board · Class 9 · Mathematics
Real Numbers revision notes for Maharashtra Board Class 9 Mathematics: 4 topics in quick points. Includes Number Systems – Hierarchy and Recall.
45 questions25 flashcards11 formulas & key relations5 concepts
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Key Topics to Revise
1
Number Systems – Hierarchy and Recall
- Natural numbers (N) = {1, 2, 3, 4, …} — counting numbers.
- Whole numbers (W) = {0, 1, 2, 3, …} — natural numbers plus zero.
- Integers (I) = {…, −3, −2, −1, 0, 1, 2, 3, …} — positive, negative, and zero.
2
Properties of Rational Numbers
- Commutative Property (Addition): a + b = b + a for all rational a, b.
- Commutative Property (Multiplication): a × b = b × a for all rational a, b.
- Associative Property (Addition): (a + b) + c = a + (b + c).
3
Decimal Forms of Rational Numbers and Converting Recurring Decimals
- Every rational number in decimal form is either TERMINATING or NON-TERMINATING RECURRING.
- Terminating decimals: denominator's prime factors are only 2 or 5 (e.g., 2/5 = 0.4, 101/8 = 12.625).
- Non-terminating recurring: denominator has prime factors other than 2 or 5 (e.g., 17/36 = 0.4722…).
4
Irrational Numbers and Real Numbers
- A number whose decimal expansion is non-terminating AND non-recurring is an irrational number.
- Examples: √2 = 1.41421…, √3 = 1.73205…, π = 3.14159…
- Proof that √2 is irrational uses contradiction method (indirect proof) — very important for exams.
Get complete notes with diagrams and examples
Full NotesKey Concepts
Rational numbers are numbers that canIrrational numbers are real numbersWe prove √2 is irrational usingA surd is an irrational rootA surd is in simplest form
Frequently Asked Questions
What are the important topics in Real Numbers for Maharashtra Board Class 9 Mathematics?
Key topics in Real Numbers include Number Systems – Hierarchy and Recall, Properties of Rational Numbers, Decimal Forms of Rational Numbers and Converting Recurring Decimals, Irrational Numbers and Real Numbers. Study these first, then practise questions on each for Class 9 exams.
How should I revise Real Numbers for Class 9 exams?
Learn the core ideas first, then work through the 45 practice questions on Real Numbers. 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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