{
  "title": "Decimal Expansions of Real Numbers - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What type of decimal expansion does 3/8 have?", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "None"}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "The decimal expansion of 7/10 is:", "options": {"A": "0.7", "B": "0.07", "C": "0.007", "D": "7.0"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "Which has terminating decimal: 1/3 or 1/4?", "options": {"A": "1/3", "B": "1/4", "C": "Both", "D": "None"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "Decimal form of 1/2 is:", "options": {"A": "0.2", "B": "0.5", "C": "0.1", "D": "0.05"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "5/16 as decimal is:", "options": {"A": "0.3125", "B": "0.5125", "C": "0.4125", "D": "0.2125"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "3/4 as decimal:", "options": {"A": "0.25", "B": "0.5", "C": "0.75", "D": "0.3"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "Which fraction gives terminating decimal: denominator 5 or 3?", "options": {"A": "5", "B": "3", "C": "Both", "D": "None"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "Decimal expansion of 9/20:", "options": {"A": "0.45", "B": "0.35", "C": "0.55", "D": "0.65"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "1/8 as decimal:", "options": {"A": "0.125", "B": "0.25", "C": "0.375", "D": "0.5"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Which is non-terminating: 2/5 or 2/3?", "options": {"A": "2/5", "B": "2/3", "C": "Both", "D": "None"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "13/25 as decimal:", "options": {"A": "0.52", "B": "0.48", "C": "0.56", "D": "0.64"}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "Decimal of 17/50:", "options": {"A": "0.34", "B": "0.32", "C": "0.36", "D": "0.38"}, "correct_answer": "A"},
    {"id": 13, "difficulty": "easy", "question": "Which denominator ensures terminating decimal: 2,3, or 7?", "options": {"A": "2", "B": "3", "C": "7", "D": "All"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "7/8 as decimal:", "options": {"A": "0.875", "B": "0.775", "C": "0.975", "D": "0.675"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "11/40 as decimal:", "options": {"A": "0.275", "B": "0.375", "C": "0.475", "D": "0.575"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Decimal expansion type of √2:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "None"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "3/5 as decimal:", "options": {"A": "0.4", "B": "0.5", "C": "0.6", "D": "0.7"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "Which has non-terminating repeating decimal: 1/7 or 1/16?", "options": {"A": "1/7", "B": "1/16", "C": "Both", "D": "None"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "19/80 as decimal:", "options": {"A": "0.2375", "B": "0.3375", "C": "0.4375", "D": "0.5375"}, "correct_answer": "A"},
    {"id": 20, "difficulty": "easy", "question": "Decimal type of π:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "None"}, "correct_answer": "C"},
    
    {"id": 21, "difficulty": "medium", "question": "Without actual division, determine decimal type of 13/125.", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Can't determine"}, "correct_answer": "A"},
    {"id": 22, "difficulty": "medium", "question": "What can you say about decimal expansion of 17/90?", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Integer"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "After how many decimal places will 3/16 terminate?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 24, "difficulty": "medium", "question": "Decimal expansion of 47/(2³×5²) will terminate after how many places?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 25, "difficulty": "medium", "question": "Which will have non-terminating decimal: 7/15 or 11/40?", "options": {"A": "7/15", "B": "11/40", "C": "Both", "D": "None"}, "correct_answer": "A"},
    {"id": 26, "difficulty": "medium", "question": "Write 0.375 as fraction in simplest form.", "options": {"A": "3/8", "B": "5/16", "C": "7/20", "D": "9/25"}, "correct_answer": "A"},
    {"id": 27, "difficulty": "medium", "question": "Express 0.777... as fraction.", "options": {"A": "7/9", "B": "7/10", "C": "77/99", "D": "77/100"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "Convert 0.125125125... to p/q form.", "options": {"A": "125/999", "B": "125/1000", "C": "125/900", "D": "125/990"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Which denominator gives terminating decimal: 2³×5 or 2×3²?", "options": {"A": "2³×5", "B": "2×3²", "C": "Both", "D": "None"}, "correct_answer": "A"},
    {"id": 30, "difficulty": "medium", "question": "Decimal expansion of 1/7 repeats after how many digits?", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 31, "difficulty": "medium", "question": "Write 0.666... as fraction.", "options": {"A": "2/3", "B": "6/9", "C": "66/99", "D": "6/10"}, "correct_answer": "A"},
    {"id": 32, "difficulty": "medium", "question": "Express 2.45 (bar on 45) as fraction.", "options": {"A": "243/99", "B": "243/100", "C": "245/99", "D": "245/100"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Which has terminating decimal: 31/375 or 17/40?", "options": {"A": "31/375", "B": "17/40", "C": "Both", "D": "None"}, "correct_answer": "B"},
    {"id": 34, "difficulty": "medium", "question": "Decimal of 23/(2²×5³) terminates after how many places?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "Write 0.2727... as fraction.", "options": {"A": "3/11", "B": "27/99", "C": "2727/9999", "D": "27/100"}, "correct_answer": "A"},
    {"id": 36, "difficulty": "medium", "question": "Express 1.2343434... as fraction.", "options": {"A": "1222/990", "B": "1234/999", "C": "1221/990", "D": "1234/9900"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "After how many places will 7/(2⁴×5²) terminate?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "Which rational number has decimal expansion 0.142857142857...?", "options": {"A": "1/6", "B": "1/7", "C": "1/8", "D": "1/9"}, "correct_answer": "B"},
    {"id": 39, "difficulty": "medium", "question": "Convert 0.16 (bar on 6) to fraction.", "options": {"A": "1/6", "B": "5/30", "C": "15/90", "D": "1/6 (simplest)"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "Decimal type of 19/21:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Integer"}, "correct_answer": "B"},
    {"id": 41, "difficulty": "medium", "question": "Write 0.08 as fraction in lowest terms.", "options": {"A": "2/25", "B": "4/50", "C": "8/100", "D": "1/12"}, "correct_answer": "A"},
    {"id": 42, "difficulty": "medium", "question": "Express 0.428571428571... as fraction.", "options": {"A": "3/7", "B": "4/9", "C": "428571/999999", "D": "3/7 (simplest)"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "After how many decimal places does 11/64 terminate?", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "medium", "question": "Which has non-terminating repeating: 5/12 or 7/25?", "options": {"A": "5/12", "B": "7/25", "C": "Both", "D": "None"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Write 0.123123123... as fraction.", "options": {"A": "41/333", "B": "123/999", "C": "123/1000", "D": "41/333 (simplest)"}, "correct_answer": "D"},
    {"id": 46, "difficulty": "medium", "question": "Express 2.317317317... as fraction.", "options": {"A": "2317/999", "B": "2315/999", "C": "2317/1000", "D": "2315/999 (simplified)"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "Decimal type of 33/55:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Integer"}, "correct_answer": "A"},
    {"id": 48, "difficulty": "medium", "question": "Write 0.009 as fraction.", "options": {"A": "9/1000", "B": "9/100", "C": "9/10", "D": "9/10000"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Express 0.58333... as fraction.", "options": {"A": "7/12", "B": "35/60", "C": "58333/99999", "D": "7/12 (simplest)"}, "correct_answer": "A"},
    {"id": 50, "difficulty": "medium", "question": "After how many places will 13/(2³×5⁴) terminate?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 51, "difficulty": "medium", "question": "Which gives terminating decimal: p/q where q=2²×5³ or q=2×3×7?", "options": {"A": "2²×5³", "B": "2×3×7", "C": "Both", "D": "None"}, "correct_answer": "A"},
    {"id": 52, "difficulty": "medium", "question": "Write 1.25 as fraction.", "options": {"A": "5/4", "B": "125/100", "C": "25/20", "D": "5/4 (simplest)"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "medium", "question": "Express 0.09 (bar on 09) as fraction.", "options": {"A": "1/11", "B": "9/99", "C": "9/100", "D": "1/11 (simplest)"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Decimal type of 41/60:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Integer"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "After how many decimal places will 7/80 terminate?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "Write 0.0016 as fraction.", "options": {"A": "1/625", "B": "16/10000", "C": "4/2500", "D": "1/625 (simplest)"}, "correct_answer": "D"},
    {"id": 57, "difficulty": "medium", "question": "Express 0.153846153846... as fraction.", "options": {"A": "2/13", "B": "153846/999999", "C": "1/6.5", "D": "2/13 (simplest)"}, "correct_answer": "A"},
    {"id": 58, "difficulty": "medium", "question": "Decimal type of 27/45:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Integer"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Write 0.00032 as fraction.", "options": {"A": "2/6250", "B": "32/100000", "C": "1/3125", "D": "1/3125 (simplest)"}, "correct_answer": "D"},
    {"id": 60, "difficulty": "medium", "question": "Express 1.08333... as fraction.", "options": {"A": "13/12", "B": "65/60", "C": "108333/100000", "D": "13/12 (simplest)"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "After how many places does 3/32 terminate?", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "Which has non-terminating: 13/65 or 17/34?", "options": {"A": "13/65", "B": "17/34", "C": "Both", "D": "None"}, "correct_answer": "D"},
    {"id": 63, "difficulty": "medium", "question": "Write 0.004 as fraction.", "options": {"A": "1/250", "B": "4/1000", "C": "2/500", "D": "1/250 (simplest)"}, "correct_answer": "D"},
    {"id": 64, "difficulty": "medium", "question": "Express 0.076923076923... as fraction.", "options": {"A": "1/13", "B": "76923/999999", "C": "2/26", "D": "1/13 (simplest)"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Decimal type of 51/75:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Integer"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "After how many places will 9/400 terminate?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "Write 0.0625 as fraction.", "options": {"A": "1/16", "B": "625/10000", "C": "5/80", "D": "1/16 (simplest)"}, "correct_answer": "D"},
    {"id": 68, "difficulty": "medium", "question": "Express 2.16 (bar on 6) as fraction.", "options": {"A": "13/6", "B": "65/30", "C": "216/99", "D": "13/6 (simplest)"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Decimal type of 22/7:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Integer"}, "correct_answer": "B"},
    {"id": 70, "difficulty": "medium", "question": "After how many places does 5/64 terminate?", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
    {"id": 71, "difficulty": "medium", "question": "Write 0.015625 as fraction.", "options": {"A": "1/64", "B": "15625/1000000", "C": "5/320", "D": "1/64 (simplest)"}, "correct_answer": "D"},
    {"id": 72, "difficulty": "medium", "question": "Express 0.571428571428... as fraction.", "options": {"A": "4/7", "B": "571428/999999", "C": "8/14", "D": "4/7 (simplest)"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "Decimal type of 35/56:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Integer"}, "correct_answer": "A"},
    {"id": 74, "difficulty": "medium", "question": "After how many places will 11/160 terminate?", "options": {"A": "3", "B": "4", "C": "5", "D": "6"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "Write 0.001 as fraction.", "options": {"A": "1/1000", "B": "1/100", "C": "1/10", "D": "1/10000"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Express 0.8333... as fraction.", "options": {"A": "5/6", "B": "25/30", "C": "8333/10000", "D": "5/6 (simplest)"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "Decimal type of 49/70:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Integer"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "After how many places does 3/125 terminate?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "Write 0.00001 as fraction.", "options": {"A": "1/100000", "B": "1/10000", "C": "1/1000", "D": "1/100"}, "correct_answer": "A"},
    {"id": 80, "difficulty": "medium", "question": "Express 1.333... as fraction.", "options": {"A": "4/3", "B": "1333/1000", "C": "40/30", "D": "4/3 (simplest)"}, "correct_answer": "D"},
    
    {"id": 81, "difficulty": "hard", "question": "If decimal expansion of p/q terminates, which must be true about q?", "options": {"A": "q=2^m×5^n", "B": "q prime", "C": "q odd", "D": "q even"}, "correct_answer": "A"},
    {"id": 82, "difficulty": "hard", "question": "Express 0.329 as fraction where 9 has bar.", "options": {"A": "329/999", "B": "329/1000", "C": "329/900", "D": "329/990"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "Find rational form of 2.13444...", "options": {"A": "1921/900", "B": "2134/999", "C": "2134/1000", "D": "1921/900 (simplified)"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Decimal expansion of √3 is:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "None"}, "correct_answer": "C"},
    {"id": 85, "difficulty": "hard", "question": "Write 3.142857142857... as fraction.", "options": {"A": "22/7", "B": "3142857/999999", "C": "3 1/7", "D": "22/7 (simplest)"}, "correct_answer": "D"},
    {"id": 86, "difficulty": "hard", "question": "If x=0.999..., then 10x-x equals:", "options": {"A": "8.999...", "B": "9", "C": "9.999...", "D": "1"}, "correct_answer": "B"},
    {"id": 87, "difficulty": "hard", "question": "Express 5.123123123... as fraction.", "options": {"A": "5123/999", "B": "5128/999", "C": "5 123/999", "D": "5128/999 (simplest)"}, "correct_answer": "B"},
    {"id": 88, "difficulty": "hard", "question": "Decimal type of cube root of 2:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Integer"}, "correct_answer": "C"},
    {"id": 89, "difficulty": "hard", "question": "Write 0.123456789101112... as fraction type.", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Cannot determine"}, "correct_answer": "B"},
    {"id": 90, "difficulty": "hard", "question": "Express 1.234567891011... as decimal type.", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Integer"}, "correct_answer": "C"},
    {"id": 91, "difficulty": "hard", "question": "Decimal expansion of e (Euler's number):", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Unknown"}, "correct_answer": "C"},
    {"id": 92, "difficulty": "hard", "question": "If 0.a1a2a3... repeating, it represents rational number. True/False?", "options": {"A": "True", "B": "False", "C": "Sometimes", "D": "Cannot say"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Write 0.101001000100001... as decimal type.", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Integer"}, "correct_answer": "C"},
    {"id": 94, "difficulty": "hard", "question": "Decimal expansion of golden ratio φ:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "1.618 exactly"}, "correct_answer": "C"},
    {"id": 95, "difficulty": "hard", "question": "Express 0.01001000100001... as fraction possibility.", "options": {"A": "Can be expressed as p/q", "B": "Cannot be expressed as p/q", "C": "Sometimes", "D": "Always rational"}, "correct_answer": "B"},
    {"id": 96, "difficulty": "hard", "question": "Decimal type of √(2/3):", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Integer"}, "correct_answer": "C"},
    {"id": 97, "difficulty": "hard", "question": "If x=0.123456789101112..., then x is:", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Natural"}, "correct_answer": "B"},
    {"id": 98, "difficulty": "hard", "question": "Decimal expansion of log₁₀2:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "0.3010 exactly"}, "correct_answer": "C"},
    {"id": 99, "difficulty": "hard", "question": "Write 1.414213562... (√2) as decimal classification.", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "Rational"}, "correct_answer": "C"},
    {"id": 100, "difficulty": "hard", "question": "Decimal type of π/2:", "options": {"A": "Terminating", "B": "Non-terminating repeating", "C": "Non-terminating non-repeating", "D": "1.5708 exactly"}, "correct_answer": "C"}
  ]
}