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Real Numbers

Maharashtra Board · Class 9 · Mathematics

Complete topic list for Real Numbers in Maharashtra Board Class 9 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

45 questions25 flashcards5 concepts

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4 Topics · Maharashtra Board Class 9 Mathematics

Topics in Real Numbers

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.

Key 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 Hierarchical classification showing how different number sets fit within real numbers, Two-branch diagram showing properties for both addition and multiplication operations, Decision tree for determining if a rational number's decimal is terminating or recurring. These are the concepts Maharashtra Board Class 9 examiners draw on most — study them first, then practise related questions.
How to score full marks in Real Numbers — Maharashtra Board Class 9 Mathematics?
Understand the core concepts first, then work through the 45 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.

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All 16 chapters — Maharashtra Board Class 9 Mathematics Syllabus

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