Number System
NIOS · Class 10 · Maths
Flashcards for Number System — NIOS Class 10 Maths. Quick Q&A cards covering key concepts, definitions, and formulas.
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Explore the full setClassify the following numbers: -17, 15, 0, -6, 22. Identify which are (i) Natural numbers (ii) Whole numbers (iii) Integers
Answer
Step 1: Natural numbers = {1, 2, 3, ...}. From given: 15, 22. Step 2: Whole numbers = {0, 1, 2, 3, ...}. From given: 0, 15, 22. Step 3: Integers = {..., -2, -1, 0, 1, 2, ...}. From given: All numbers …
Express 18/27 in its lowest terms (standard form)
Answer
Step 1: Find GCD of 18 and 27. Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. GCD = 9. Step 2: Divide both numerator and denominator by GCD. 18 ÷ 9 = 2, 27 ÷ 9 = 3. Answer: 2/3. The rat…
Add the rational numbers: 3/4 + 2/3
Answer
Step 1: Find LCM of denominators 4 and 3. LCM(4,3) = 12. Step 2: Convert to equivalent fractions. 3/4 = (3×3)/(4×3) = 9/12. 2/3 = (2×4)/(3×4) = 8/12. Step 3: Add numerators. 9/12 + 8/12 = (9+8)/12 = 1…
Multiply: (-5/6) × (3/7)
Answer
Step 1: Apply multiplication rule for rational numbers. (p/q) × (r/s) = (p×r)/(q×s). Step 2: Multiply numerators and denominators. (-5/6) × (3/7) = (-5×3)/(6×7) = -15/42. Step 3: Reduce to lowest term…
Convert 7/8 to decimal form
Answer
Step 1: Perform long division of 7 ÷ 8. Step 2: 7.000 ÷ 8. 8 goes into 70 eight times (8×8=64), remainder 6. 8 goes into 60 seven times (8×7=56), remainder 4. 8 goes into 40 five times exactly. Step 3…
Convert 5/11 to decimal form and identify the type
Answer
Step 1: Perform long division 5 ÷ 11. Step 2: 5.000000... ÷ 11. Pattern: 11 goes into 50 four times (remainder 6), into 60 five times (remainder 5). When remainder becomes 5 again, pattern repeats. St…
Express 0.75 in p/q form
Answer
Step 1: Write as fraction over appropriate power of 10. 0.75 = 75/100. Step 2: Reduce to lowest terms by finding GCD. GCD(75,100) = 25. Step 3: Divide both by GCD. 75÷25 = 3, 100÷25 = 4. Answer: 0.75 …
Express 0.666... (0.6̄) in p/q form
Answer
Step 1: Let x = 0.666... Step 2: Multiply by 10: 10x = 6.666... Step 3: Subtract original equation: 10x - x = 6.666... - 0.666... → 9x = 6. Step 4: Solve for x: x = 6/9 = 2/3. Answer: 0.6̄ = 2/3. Veri…
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