Real Numbers — Flashcards
Maharashtra Board · Class 9 · Mathematics
25 flashcards for Real Numbers (Maharashtra Board Class 9 Mathematics) to test yourself on key terms and facts.
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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 …
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…
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…
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…
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…
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 (…
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…
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…
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