Skip to main content
Chapter 3 of 16
Flashcards

Real Numbers

Maharashtra Board · Class 9 · Mathematics

Flashcards for Real Numbers — Maharashtra Board Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.

45 questions25 flashcards5 concepts

Interactive on Super Tutor

Studying Real Numbers? Get the full interactive chapter.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for flashcards and more.

1,000+ Class 9 students started this chapter today

25 Flashcards
Card 1Properties of Rational Numbers

Identify which numbers are rational: √2, 5/7, 0, -3, π, 2.5, 1.333...(repeating)

Answer

Rational numbers: 5/7, 0, -3, 2.5, 1.333...(repeating) Explanation: A rational number is any number that can be expressed as p/q where p and q are integers and q ≠ 0. - 5/7 is already in p/q form - 0

Card 2Properties of Rational Numbers

Convert the repeating decimal 2.3̄ (2.3333...) into p/q form

Answer

Step 1: Let x = 2.3̄ = 2.3333... Step 2: Since one digit (3) repeats, multiply by 10: 10x = 23.3333... Step 3: Subtract: 10x - x = 23.3333... - 2.3333... 9x = 21 Step 4: Solve for x: x = 21/9 = 7/3 An

Card 3Properties of Rational Numbers

Convert the repeating decimal 1.24̄ (1.2444...) into p/q form

Answer

Step 1: Let x = 1.24̄ = 1.2444... Step 2: Since the digit 4 repeats, but 2 doesn't, multiply by 100 (two decimal places before repeat): 100x = 124.444... Step 3: Also multiply by 10: 10x = 12.444... S

Card 4Properties of Rational Numbers

Compare 3/5 and 5/8 using the order relation rule for rational numbers

Answer

Given: p/q = 3/5 and r/s = 5/8 (both denominators positive) Method: Compare p×s with q×r Step 1: p × s = 3 × 8 = 24 Step 2: q × r = 5 × 5 = 25 Step 3: Since 24 < 25, we have p×s < q×r Step 4: Therefor

Card 5Properties of Irrational Numbers

Why is √2 an irrational number? Prove by contradiction

Answer

Proof by Contradiction: Assume: √2 is rational, so √2 = p/q (where p and q have no common factors) Step 1: Square both sides: 2 = p²/q² → 2q² = p² Step 2: Since 2q² = p², p² is even Step 3: If p² is e

Card 6Properties of Irrational Numbers

Determine if 2 + √3 is rational or irrational. Justify your answer

Answer

Answer: 2 + √3 is IRRATIONAL Proof: Step 1: Assume 2 + √3 is rational Step 2: Then 2 + √3 = r (where r is some rational number) Step 3: Rearranging: √3 = r - 2 Step 4: Right side (r - 2) is rational (

Card 7Simplest Form of Surds

Simplify √48 to its simplest form

Answer

Step 1: Factor 48 into prime factors and perfect squares: 48 = 16 × 3 = 4² × 3 Step 2: Apply √(ab) = √a × √b: √48 = √(16 × 3) = √16 × √3 Step 3: Simplify √16: √16 = 4 Step 4: Final answer: √48 = 4√3 V

Card 8Simplest Form of Surds

Simplify √98 to its simplest form

Answer

Step 1: Find perfect square factors of 98: 98 = 2 × 49 = 2 × 7² Step 2: Apply √(ab) = √a × √b: √98 = √(49 × 2) = √49 × √2 Step 3: Simplify √49: √49 = 7 Step 4: Final answer: √98 = 7√2 Verification: (7

+17 more flashcards available

Practice All

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.
How many flashcards are available for Real Numbers?
There are 25 flashcards for Real Numbers covering key definitions, formulas, and concepts. Use them daily for 10–15 minutes for best results.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

For serious students

Get the full Real Numbers chapter — for free.

Quizzes, flashcards, AI doubt-solver and a step-by-step study plan for Maharashtra Board Class 9 Mathematics.