{
  "title": "Real Numbers and their Decimal Expansions - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "The decimal expansion of 1/2 is:", "options": {"A": "0.5", "B": "0.50", "C": "0.5...", "D": "0.499..."}, "correct_answer": "A"},
    {"id": 2, "difficulty": "easy", "question": "1/3 in decimal form is:", "options": {"A": "0.3", "B": "0.33", "C": "0.333...", "D": "0.34"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "A terminating decimal has:", "options": {"A": "Infinite digits", "B": "Finite digits", "C": "Repeating pattern", "D": "No decimal point"}, "correct_answer": "B"},
    {"id": 4, "difficulty": "easy", "question": "Which is a non-terminating decimal?", "options": {"A": "0.25", "B": "0.333...", "C": "0.75", "D": "0.625"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "The decimal for 1/4 is:", "options": {"A": "0.25", "B": "0.2", "C": "0.250", "D": "0.255..."}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "A repeating decimal is also called:", "options": {"A": "Terminating", "B": "Recurring", "C": "Irrational", "D": "Non-decimal"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "0.666... represents:", "options": {"A": "2/3", "B": "1/3", "C": "3/2", "D": "6/9"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "The decimal 0.5 is:", "options": {"A": "Terminating", "B": "Non-terminating", "C": "Recurring", "D": "Irrational"}, "correct_answer": "A"},
    {"id": 9, "difficulty": "easy", "question": "1/8 as decimal is:", "options": {"A": "0.125", "B": "0.12", "C": "0.124...", "D": "0.13"}, "correct_answer": "A"},
    {"id": 10, "difficulty": "easy", "question": "Which decimal terminates?", "options": {"A": "0.121212...", "B": "0.123123...", "C": "0.125", "D": "0.333..."}, "correct_answer": "C"},
    {"id": 11, "difficulty": "easy", "question": "The decimal for 3/4 is:", "options": {"A": "0.75", "B": "0.7", "C": "0.750", "D": "0.749..."}, "correct_answer": "A"},
    {"id": 12, "difficulty": "easy", "question": "0.999... equals:", "options": {"A": "0.9", "B": "1", "C": "0.99", "D": "0.999"}, "correct_answer": "B"},
    {"id": 13, "difficulty": "easy", "question": "A non-terminating, non-repeating decimal represents:", "options": {"A": "Rational", "B": "Irrational", "C": "Integer", "D": "Fraction"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "1/5 as decimal:", "options": {"A": "0.2", "B": "0.20", "C": "0.199...", "D": "0.25"}, "correct_answer": "A"},
    {"id": 15, "difficulty": "easy", "question": "Which is recurring?", "options": {"A": "0.25", "B": "0.250", "C": "0.2525...", "D": "0.255"}, "correct_answer": "C"},
    {"id": 16, "difficulty": "easy", "question": "The decimal for 2/5 is:", "options": {"A": "0.4", "B": "0.40", "C": "0.399...", "D": "0.45"}, "correct_answer": "A"},
    {"id": 17, "difficulty": "easy", "question": "0.333... × 3 =", "options": {"A": "0.999...", "B": "1", "C": "0.9", "D": "Both A and B"}, "correct_answer": "D"},
    {"id": 18, "difficulty": "easy", "question": "1/10 as decimal:", "options": {"A": "0.1", "B": "0.10", "C": "0.099...", "D": "0.11"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "A terminating decimal can be written as fraction with denominator as power of:", "options": {"A": "2", "B": "5", "C": "10", "D": "2 or 5"}, "correct_answer": "D"},
    {"id": 20, "difficulty": "easy", "question": "0.75 equals fraction:", "options": {"A": "3/4", "B": "75/100", "C": "7.5/10", "D": "All of these"}, "correct_answer": "D"},

    {"id": 21, "difficulty": "medium", "question": "Convert 0.125 to fraction", "options": {"A": "1/8", "B": "125/1000", "C": "1/4", "D": "A and B"}, "correct_answer": "D"},
    {"id": 22, "difficulty": "medium", "question": "The decimal expansion of √2 is:", "options": {"A": "1.41421356... non-repeating", "B": "1.41421356... repeating", "C": "1.414, terminating", "D": "1.41, terminating"}, "correct_answer": "A"},
    {"id": 23, "difficulty": "medium", "question": "Express 0.777... as fraction", "options": {"A": "7/9", "B": "77/99", "C": "777/999", "D": "All of these"}, "correct_answer": "D"},
    {"id": 24, "difficulty": "medium", "question": "Which has terminating decimal? 3/16", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Can't say"}, "correct_answer": "A"},
    {"id": 25, "difficulty": "medium", "question": "Convert 1.272727... to fraction", "options": {"A": "14/11", "B": "127/99", "C": "1.27/1", "D": "A and B"}, "correct_answer": "D"},
    {"id": 26, "difficulty": "medium", "question": "The decimal for π is:", "options": {"A": "3.14, terminating", "B": "3.14159..., non-repeating", "C": "3.14159..., repeating", "D": "22/7"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "Express 0.363636... as fraction", "options": {"A": "4/11", "B": "36/99", "C": "3636/9999", "D": "All of these"}, "correct_answer": "D"},
    {"id": 28, "difficulty": "medium", "question": "Which terminates? 7/25", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Sometimes"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "Convert 2.333... to mixed fraction", "options": {"A": "2 1/3", "B": "7/3", "C": "21/9", "D": "All of these"}, "correct_answer": "D"},
    {"id": 30, "difficulty": "medium", "question": "√3 as decimal:", "options": {"A": "1.7320508... non-repeating", "B": "1.732, terminating", "C": "1.73, repeating", "D": "1.7320508... repeating"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "Express 0.123123... as fraction", "options": {"A": "41/333", "B": "123/999", "C": "123123/999999", "D": "All of these"}, "correct_answer": "D"},
    {"id": 32, "difficulty": "medium", "question": "Which terminates? 11/40", "options": {"A": "Yes", "B": "No", "C": "Depends", "D": "Never"}, "correct_answer": "A"},
    {"id": 33, "difficulty": "medium", "question": "Convert 0.1666... to fraction", "options": {"A": "1/6", "B": "1666/9999", "C": "0.16/0.99", "D": "A and B"}, "correct_answer": "D"},
    {"id": 34, "difficulty": "medium", "question": "The decimal for √5:", "options": {"A": "2.2360679... non-repeating", "B": "2.236, terminating", "C": "2.24, repeating", "D": "2.2360679... repeating"}, "correct_answer": "A"},
    {"id": 35, "difficulty": "medium", "question": "Express 0.454545... as fraction", "options": {"A": "5/11", "B": "45/99", "C": "4545/9999", "D": "All of these"}, "correct_answer": "D"},
    {"id": 36, "difficulty": "medium", "question": "Which terminates? 13/125", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Undefined"}, "correct_answer": "A"},
    {"id": 37, "difficulty": "medium", "question": "Convert 1.08333... to fraction", "options": {"A": "13/12", "B": "1.08/1.00", "C": "108333/99999", "D": "All of these"}, "correct_answer": "A"},
    {"id": 38, "difficulty": "medium", "question": "√7 as decimal:", "options": {"A": "2.64575131... non-repeating", "B": "2.645, terminating", "C": "2.65, repeating", "D": "2.64575131... repeating"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "Express 0.571428571428... as fraction", "options": {"A": "4/7", "B": "571428/999999", "C": "0.571428/0.999999", "D": "All of these"}, "correct_answer": "D"},
    {"id": 40, "difficulty": "medium", "question": "Which terminates? 17/80", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Can't determine"}, "correct_answer": "A"},
    {"id": 41, "difficulty": "medium", "question": "Convert 0.8333... to fraction", "options": {"A": "5/6", "B": "8333/9999", "C": "0.83/1", "D": "All of these"}, "correct_answer": "D"},
    {"id": 42, "difficulty": "medium", "question": "The decimal for √11:", "options": {"A": "3.31662479... non-repeating", "B": "3.3166, terminating", "C": "3.317, repeating", "D": "3.31662479... repeating"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "Express 0.285714285714... as fraction", "options": {"A": "2/7", "B": "285714/999999", "C": "0.285714/0.999999", "D": "All of these"}, "correct_answer": "D"},
    {"id": 44, "difficulty": "medium", "question": "Which terminates? 19/160", "options": {"A": "Yes", "B": "No", "C": "Only sometimes", "D": "Never"}, "correct_answer": "A"},
    {"id": 45, "difficulty": "medium", "question": "Convert 0.1333... to fraction", "options": {"A": "2/15", "B": "1333/9999", "C": "0.13/0.99", "D": "All of these"}, "correct_answer": "D"},
    {"id": 46, "difficulty": "medium", "question": "√13 as decimal:", "options": {"A": "3.605551275... non-repeating", "B": "3.605, terminating", "C": "3.61, repeating", "D": "3.605551275... repeating"}, "correct_answer": "A"},
    {"id": 47, "difficulty": "medium", "question": "Express 0.384615384615... as fraction", "options": {"A": "5/13", "B": "384615/999999", "C": "0.384615/0.999999", "D": "All of these"}, "correct_answer": "D"},
    {"id": 48, "difficulty": "medium", "question": "Which terminates? 23/200", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Depends on base"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "Convert 0.2666... to fraction", "options": {"A": "4/15", "B": "2666/9999", "C": "0.26/0.99", "D": "All of these"}, "correct_answer": "D"},
    {"id": 50, "difficulty": "medium", "question": "√17 as decimal:", "options": {"A": "4.123105626... non-repeating", "B": "4.123, terminating", "C": "4.12, repeating", "D": "4.123105626... repeating"}, "correct_answer": "A"},
    {"id": 51, "difficulty": "medium", "question": "Express 0.692307692307... as fraction", "options": {"A": "9/13", "B": "692307/999999", "C": "0.692307/0.999999", "D": "All of these"}, "correct_answer": "D"},
    {"id": 52, "difficulty": "medium", "question": "Which terminates? 29/250", "options": {"A": "Yes", "B": "No", "C": "Only if simplified", "D": "Never"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "Convert 0.9333... to fraction", "options": {"A": "14/15", "B": "9333/9999", "C": "0.93/1", "D": "All of these"}, "correct_answer": "D"},
    {"id": 54, "difficulty": "medium", "question": "√19 as decimal:", "options": {"A": "4.358898944... non-repeating", "B": "4.359, terminating", "C": "4.36, repeating", "D": "4.358898944... repeating"}, "correct_answer": "A"},
    {"id": 55, "difficulty": "medium", "question": "Express 0.2352941176470588... as fraction", "options": {"A": "4/17", "B": "2352941176470588/9999999999999999", "C": "0.2352941176470588/0.9999999999999999", "D": "All of these"}, "correct_answer": "D"},
    {"id": 56, "difficulty": "medium", "question": "Which terminates? 31/320", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Not sure"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Convert 0.0666... to fraction", "options": {"A": "1/15", "B": "666/9999", "C": "0.06/0.99", "D": "All of these"}, "correct_answer": "D"},
    {"id": 58, "difficulty": "medium", "question": "√23 as decimal:", "options": {"A": "4.795831523... non-repeating", "B": "4.7958, terminating", "C": "4.796, repeating", "D": "4.795831523... repeating"}, "correct_answer": "A"},
    {"id": 59, "difficulty": "medium", "question": "Express 0.210526315789473684... as fraction", "options": {"A": "4/19", "B": "210526315789473684/999999999999999999", "C": "0.210526315789473684/0.999999999999999999", "D": "All of these"}, "correct_answer": "D"},
    {"id": 60, "difficulty": "medium", "question": "Which terminates? 37/400", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Only in some bases"}, "correct_answer": "A"},
    {"id": 61, "difficulty": "medium", "question": "Convert 0.4666... to fraction", "options": {"A": "7/15", "B": "4666/9999", "C": "0.46/0.99", "D": "All of these"}, "correct_answer": "D"},
    {"id": 62, "difficulty": "medium", "question": "√29 as decimal:", "options": {"A": "5.385164807... non-repeating", "B": "5.385, terminating", "C": "5.39, repeating", "D": "5.385164807... repeating"}, "correct_answer": "A"},
    {"id": 63, "difficulty": "medium", "question": "Express 0.148148148... as fraction", "options": {"A": "4/27", "B": "148/999", "C": "148148/999999", "D": "All of these"}, "correct_answer": "D"},
    {"id": 64, "difficulty": "medium", "question": "Which terminates? 41/500", "options": {"A": "Yes", "B": "No", "C": "Depends on representation", "D": "Never"}, "correct_answer": "A"},
    {"id": 65, "difficulty": "medium", "question": "Convert 0.8666... to fraction", "options": {"A": "13/15", "B": "8666/9999", "C": "0.86/0.99", "D": "All of these"}, "correct_answer": "D"},
    {"id": 66, "difficulty": "medium", "question": "√31 as decimal:", "options": {"A": "5.567764363... non-repeating", "B": "5.5678, terminating", "C": "5.568, repeating", "D": "5.567764363... repeating"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "Express 0.189189189... as fraction", "options": {"A": "7/37", "B": "189/999", "C": "189189/999999", "D": "All of these"}, "correct_answer": "D"},
    {"id": 68, "difficulty": "medium", "question": "Which terminates? 43/625", "options": {"A": "Yes", "B": "No", "C": "Only if decimal", "D": "Sometimes"}, "correct_answer": "A"},
    {"id": 69, "difficulty": "medium", "question": "Convert 0.2333... to fraction", "options": {"A": "7/30", "B": "2333/9999", "C": "0.23/0.99", "D": "All of these"}, "correct_answer": "D"},
    {"id": 70, "difficulty": "medium", "question": "√37 as decimal:", "options": {"A": "6.08276253... non-repeating", "B": "6.0828, terminating", "C": "6.083, repeating", "D": "6.08276253... repeating"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "Express 0.108108108... as fraction", "options": {"A": "4/37", "B": "108/999", "C": "108108/999999", "D": "All of these"}, "correct_answer": "D"},
    {"id": 72, "difficulty": "medium", "question": "Which terminates? 47/800", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Undefined"}, "correct_answer": "A"},
    {"id": 73, "difficulty": "medium", "question": "Convert 0.5333... to fraction", "options": {"A": "8/15", "B": "5333/9999", "C": "0.53/0.99", "D": "All of these"}, "correct_answer": "D"},
    {"id": 74, "difficulty": "medium", "question": "√41 as decimal:", "options": {"A": "6.403124237... non-repeating", "B": "6.4031, terminating", "C": "6.403, repeating", "D": "6.403124237... repeating"}, "correct_answer": "A"},
    {"id": 75, "difficulty": "medium", "question": "Express 0.162162162... as fraction", "options": {"A": "6/37", "B": "162/999", "C": "162162/999999", "D": "All of these"}, "correct_answer": "D"},
    {"id": 76, "difficulty": "medium", "question": "Which terminates? 53/1000", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Never"}, "correct_answer": "A"},
    {"id": 77, "difficulty": "medium", "question": "Convert 0.7333... to fraction", "options": {"A": "11/15", "B": "7333/9999", "C": "0.73/0.99", "D": "All of these"}, "correct_answer": "D"},
    {"id": 78, "difficulty": "medium", "question": "√43 as decimal:", "options": {"A": "6.557438524... non-repeating", "B": "6.5574, terminating", "C": "6.557, repeating", "D": "6.557438524... repeating"}, "correct_answer": "A"},
    {"id": 79, "difficulty": "medium", "question": "Express 0.135135135... as fraction", "options": {"A": "5/37", "B": "135/999", "C": "135135/999999", "D": "All of these"}, "correct_answer": "D"},
    {"id": 80, "difficulty": "medium", "question": "Which terminates? 59/1250", "options": {"A": "Yes", "B": "No", "C": "Depends", "D": "Not always"}, "correct_answer": "A"},

    {"id": 81, "difficulty": "hard", "question": "Without actual division, determine if 129/(2²×5⁷×7⁵) has terminating decimal", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Can't determine"}, "correct_answer": "B"},
    {"id": 82, "difficulty": "hard", "question": "The decimal expansion of 1/17 has period length:", "options": {"A": "16", "B": "17", "C": "8", "D": "9"}, "correct_answer": "A"},
    {"id": 83, "difficulty": "hard", "question": "If a rational number p/q has terminating decimal, q must have prime factors:", "options": {"A": "Only 2", "B": "Only 5", "C": "Only 2 and/or 5", "D": "Any primes"}, "correct_answer": "C"},
    {"id": 84, "difficulty": "hard", "question": "The decimal for 1/7 repeats after how many digits?", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "A"},
    {"id": 85, "difficulty": "hard", "question": "Which denominator gives terminating decimal for proper fraction? 250", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Never"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "The period of 1/13 is:", "options": {"A": "6", "B": "12", "C": "13", "D": "26"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "A rational number's decimal expansion terminates if denominator (after simplification) has only:", "options": {"A": "Even numbers", "B": "Prime factors 2 or 5", "C": "Odd numbers", "D": "Prime factors other than 2,5"}, "correct_answer": "B"},
    {"id": 88, "difficulty": "hard", "question": "1/11 as decimal has period:", "options": {"A": "1", "B": "2", "C": "10", "D": "11"}, "correct_answer": "B"},
    {"id": 89, "difficulty": "hard", "question": "After how many decimal places will 3/16 terminate?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "C"},
    {"id": 90, "difficulty": "hard", "question": "The decimal for 1/19 repeats every:", "options": {"A": "18 digits", "B": "19 digits", "C": "9 digits", "D": "38 digits"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "For rational p/q, decimal terminates if q = 2^m × 5^n where m,n are:", "options": {"A": "Integers", "B": "Non-negative integers", "C": "Positive integers", "D": "Any real numbers"}, "correct_answer": "B"},
    {"id": 92, "difficulty": "hard", "question": "1/37 has period length:", "options": {"A": "3", "B": "6", "C": "9", "D": "12"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "7/125 terminates after how many decimal places?", "options": {"A": "2", "B": "3", "C": "4", "D": "5"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "The recurring block in 1/23 has length:", "options": {"A": "11", "B": "22", "C": "23", "D": "46"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "A fraction with denominator 360 will terminate?", "options": {"A": "Yes", "B": "No", "C": "Depends on numerator", "D": "360 = 2³×3²×5, so no"}, "correct_answer": "D"},
    {"id": 96, "difficulty": "hard", "question": "1/29 has period:", "options": {"A": "28", "B": "29", "C": "14", "D": "7"}, "correct_answer": "A"},
    {"id": 97, "difficulty": "hard", "question": "11/64 terminates after how many decimals?", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 98, "difficulty": "hard", "question": "The decimal for 1/31 repeats every:", "options": {"A": "15 digits", "B": "30 digits", "C": "31 digits", "D": "62 digits"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "Which will terminate? 13/(2³×5²)", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Can't say"}, "correct_answer": "A"},
    {"id": 100, "difficulty": "hard", "question": "1/47 has recurring period of:", "options": {"A": "46", "B": "47", "C": "23", "D": "13"}, "correct_answer": "A"}
  ]
}