{
  "schemaVersion": "1.0",
  "moduleId": "calculator-use-0580-pilot",
  "pathways": {
    "enter-it-right": {
      "minimumDistinctItems": 19,
      "objectiveRecordIds": [
        "0580-core-C1.14-1",
        "0580-core-C1.14-2",
        "0580-extended-E1.14-1",
        "0580-extended-E1.14-2"
      ],
      "items": [
        {
          "id": "ent-q01",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out (7.2 + 3.9) ÷ (2.4 − 1.8) on your calculator.",
          "data": {
            "family": "fraction-entry",
            "misconceptionDistractor": "7.025",
            "misconceptionDistractors": [
              {
                "value": "2.825",
                "code": "cu-brackets-missing",
                "feedback": "A long numerator or denominator needs BRACKETS: the calculator divides by only the next term otherwise."
              },
              {
                "value": "19.5",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "18.5",
          "difficulty": 1,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "Brackets around the whole numerator and the whole denominator: 18.5.",
          "misconceptionCode": "cu-brackets-missing",
          "options": [
            "18.5",
            "7.025",
            "2.825",
            "19.5"
          ],
          "correctIndex": 0
        },
        {
          "id": "ent-q02",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out (12.6 + 2.4) ÷ (9.6 − 4.6) on your calculator.",
          "data": {
            "family": "fraction-entry",
            "misconceptionDistractor": "4",
            "misconceptionDistractors": [
              {
                "value": "8.25",
                "code": "cu-brackets-missing",
                "feedback": "A long numerator or denominator needs BRACKETS: the calculator divides by only the next term otherwise."
              },
              {
                "value": "-3.0375",
                "code": "cu-brackets-missing",
                "feedback": "A long numerator or denominator needs BRACKETS: the calculator divides by only the next term otherwise."
              }
            ]
          },
          "correctAnswer": "3",
          "difficulty": 1,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "Brackets around the whole numerator and the whole denominator: 3.",
          "misconceptionCode": "cu-arithmetic",
          "options": [
            "4",
            "3",
            "8.25",
            "-3.0375"
          ],
          "correctIndex": 1
        },
        {
          "id": "ent-q03",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out (8.4 − 2.1) ÷ (1.4 + 0.7) on your calculator.",
          "data": {
            "family": "fraction-entry",
            "misconceptionDistractor": "7.6",
            "misconceptionDistractors": [
              {
                "value": "5.2",
                "code": "cu-brackets-missing",
                "feedback": "A long numerator or denominator needs BRACKETS: the calculator divides by only the next term otherwise."
              },
              {
                "value": "4",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "3",
          "difficulty": 2,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "Brackets around the whole numerator and the whole denominator: 3.",
          "misconceptionCode": "cu-brackets-missing",
          "options": [
            "5.2",
            "7.6",
            "3",
            "4"
          ],
          "correctIndex": 2
        },
        {
          "id": "ent-q04",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out (4.8 + 7.7) ÷ (6.25 − 1.25) on your calculator.",
          "data": {
            "family": "fraction-entry",
            "misconceptionDistractor": "4.782",
            "misconceptionDistractors": [
              {
                "value": "0.75",
                "code": "cu-brackets-missing",
                "feedback": "A long numerator or denominator needs BRACKETS: the calculator divides by only the next term otherwise."
              },
              {
                "value": "3.5",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "2.5",
          "difficulty": 2,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "Brackets around the whole numerator and the whole denominator: 2.5.",
          "misconceptionCode": "cu-brackets-missing",
          "options": [
            "3.5",
            "4.782",
            "0.75",
            "2.5"
          ],
          "correctIndex": 3
        },
        {
          "id": "ent-q05",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out √(9 + 16) on your calculator.",
          "data": {
            "family": "root-scope",
            "misconceptionDistractor": "19",
            "misconceptionDistractors": [
              {
                "value": "7",
                "code": "cu-root-scope",
                "feedback": "The root covers only what is inside its bracket: √(a + b) is not √a + b — open a bracket for the whole sum."
              },
              {
                "value": "6",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "5",
          "difficulty": 1,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "√(9 + 16) = √25 = 5: the root covers the whole bracket.",
          "misconceptionCode": "cu-root-scope",
          "options": [
            "5",
            "19",
            "7",
            "6"
          ],
          "correctIndex": 0
        },
        {
          "id": "ent-q06",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out √(25 + 144) on your calculator.",
          "data": {
            "family": "root-scope",
            "misconceptionDistractor": "14",
            "misconceptionDistractors": [
              {
                "value": "149",
                "code": "cu-root-scope",
                "feedback": "The root covers only what is inside its bracket: √(a + b) is not √a + b — open a bracket for the whole sum."
              },
              {
                "value": "17",
                "code": "cu-root-scope",
                "feedback": "The root covers only what is inside its bracket: √(a + b) is not √a + b — open a bracket for the whole sum."
              }
            ]
          },
          "correctAnswer": "13",
          "difficulty": 1,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "√(25 + 144) = √169 = 13: the root covers the whole bracket.",
          "misconceptionCode": "cu-arithmetic",
          "options": [
            "14",
            "13",
            "149",
            "17"
          ],
          "correctIndex": 1
        },
        {
          "id": "ent-q07",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out √(36 + 64) on your calculator.",
          "data": {
            "family": "root-scope",
            "misconceptionDistractor": "70",
            "misconceptionDistractors": [
              {
                "value": "14",
                "code": "cu-root-scope",
                "feedback": "The root covers only what is inside its bracket: √(a + b) is not √a + b — open a bracket for the whole sum."
              },
              {
                "value": "11",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "10",
          "difficulty": 2,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "√(36 + 64) = √100 = 10: the root covers the whole bracket.",
          "misconceptionCode": "cu-root-scope",
          "options": [
            "14",
            "70",
            "10",
            "11"
          ],
          "correctIndex": 2
        },
        {
          "id": "ent-q08",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out √(0.36 + 0.64) on your calculator.",
          "data": {
            "family": "root-scope",
            "misconceptionDistractor": "1.24",
            "misconceptionDistractors": [
              {
                "value": "1.4",
                "code": "cu-root-scope",
                "feedback": "The root covers only what is inside its bracket: √(a + b) is not √a + b — open a bracket for the whole sum."
              },
              {
                "value": "2",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "1",
          "difficulty": 3,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "√(0.36 + 0.64) = √1 = 1: the root covers the whole bracket.",
          "misconceptionCode": "cu-root-scope",
          "options": [
            "2",
            "1.24",
            "1.4",
            "1"
          ],
          "correctIndex": 3
        },
        {
          "id": "ent-q09",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out (−3)² on your calculator.",
          "data": {
            "family": "negative-power",
            "misconceptionDistractor": "-9",
            "misconceptionDistractors": [
              {
                "value": "-6",
                "code": "cu-minus-power",
                "feedback": "Mind the base of the power: (−3)² = 9 but −3² = −9 — the minus and the square bind differently."
              },
              {
                "value": "10",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "9",
          "difficulty": 1,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "(−3)² = 9: the bracket makes the base negative, and a negative squared is positive.",
          "misconceptionCode": "cu-minus-power",
          "options": [
            "9",
            "-9",
            "-6",
            "10"
          ],
          "correctIndex": 0
        },
        {
          "id": "ent-q10",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out (−1.5)² on your calculator.",
          "data": {
            "family": "negative-power",
            "misconceptionDistractor": "3.25",
            "misconceptionDistractors": [
              {
                "value": "-2.25",
                "code": "cu-minus-power",
                "feedback": "Mind the base of the power: (−3)² = 9 but −3² = −9 — the minus and the square bind differently."
              },
              {
                "value": "-3",
                "code": "cu-minus-power",
                "feedback": "Mind the base of the power: (−3)² = 9 but −3² = −9 — the minus and the square bind differently."
              }
            ]
          },
          "correctAnswer": "2.25",
          "difficulty": 1,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "(−1.5)² = 2.25: the bracket makes the base negative, and a negative squared is positive.",
          "misconceptionCode": "cu-arithmetic",
          "options": [
            "3.25",
            "2.25",
            "-2.25",
            "-3"
          ],
          "correctIndex": 1
        },
        {
          "id": "ent-q11",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out −2.4² on your calculator.",
          "data": {
            "family": "negative-power",
            "misconceptionDistractor": "5.76",
            "misconceptionDistractors": [
              {
                "value": "-4.8",
                "code": "cu-minus-power",
                "feedback": "Mind the base of the power: (−3)² = 9 but −3² = −9 — the minus and the square bind differently."
              },
              {
                "value": "-4.76",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "-5.76",
          "difficulty": 2,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "−2.4² = -5.76: the minus is applied AFTER the square.",
          "misconceptionCode": "cu-minus-power",
          "options": [
            "-4.8",
            "5.76",
            "-5.76",
            "-4.76"
          ],
          "correctIndex": 2
        },
        {
          "id": "ent-q12",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out (−0.6)² on your calculator.",
          "data": {
            "family": "negative-power",
            "misconceptionDistractor": "-0.36",
            "misconceptionDistractors": [
              {
                "value": "-1.2",
                "code": "cu-minus-power",
                "feedback": "Mind the base of the power: (−3)² = 9 but −3² = −9 — the minus and the square bind differently."
              },
              {
                "value": "1.36",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "0.36",
          "difficulty": 2,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "(−0.6)² = 0.36: the bracket makes the base negative, and a negative squared is positive.",
          "misconceptionCode": "cu-minus-power",
          "options": [
            "1.36",
            "-0.36",
            "-1.2",
            "0.36"
          ],
          "correctIndex": 3
        },
        {
          "id": "ent-q13",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out 1½ × 3.2 on your calculator.",
          "data": {
            "family": "mixed-number",
            "misconceptionDistractor": "1.6",
            "misconceptionDistractors": [
              {
                "value": "2.6",
                "code": "cu-mixed-number",
                "feedback": "A mixed number is a SUM (1½ = 1 + ½), not a product — enter it with the fraction key or brackets."
              },
              {
                "value": "8",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "4.8",
          "difficulty": 2,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "1½ is 1.5: 4.8.",
          "misconceptionCode": "cu-mixed-number",
          "options": [
            "4.8",
            "1.6",
            "2.6",
            "8"
          ],
          "correctIndex": 0
        },
        {
          "id": "ent-q14",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out 2½ × 1.6 on your calculator.",
          "data": {
            "family": "mixed-number",
            "misconceptionDistractor": "1.6",
            "misconceptionDistractors": [
              {
                "value": "2.8",
                "code": "cu-mixed-number",
                "feedback": "A mixed number is a SUM (1½ = 1 + ½), not a product — enter it with the fraction key or brackets."
              },
              {
                "value": "5.6",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "4",
          "difficulty": 1,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "2½ is 2.5: 4.",
          "misconceptionCode": "cu-mixed-number",
          "options": [
            "1.6",
            "4",
            "2.8",
            "5.6"
          ],
          "correctIndex": 1
        },
        {
          "id": "ent-q15",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out 3¼ × 2.4 on your calculator.",
          "data": {
            "family": "mixed-number",
            "misconceptionDistractor": "10.2",
            "misconceptionDistractors": [
              {
                "value": "1.8",
                "code": "cu-mixed-number",
                "feedback": "A mixed number is a SUM (1½ = 1 + ½), not a product — enter it with the fraction key or brackets."
              },
              {
                "value": "3.6",
                "code": "cu-mixed-number",
                "feedback": "A mixed number is a SUM (1½ = 1 + ½), not a product — enter it with the fraction key or brackets."
              }
            ]
          },
          "correctAnswer": "7.8",
          "difficulty": 2,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "3¼ is 3.25: 7.8.",
          "misconceptionCode": "cu-arithmetic",
          "options": [
            "1.8",
            "10.2",
            "7.8",
            "3.6"
          ],
          "correctIndex": 2
        },
        {
          "id": "ent-q16",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out 1¾ × 2.8 on your calculator.",
          "data": {
            "family": "mixed-number",
            "misconceptionDistractor": "2.1",
            "misconceptionDistractors": [
              {
                "value": "3.1",
                "code": "cu-mixed-number",
                "feedback": "A mixed number is a SUM (1½ = 1 + ½), not a product — enter it with the fraction key or brackets."
              },
              {
                "value": "7.7",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "4.9",
          "difficulty": 3,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "1¾ is 1.75: 4.9.",
          "misconceptionCode": "cu-mixed-number",
          "options": [
            "7.7",
            "2.1",
            "3.1",
            "4.9"
          ],
          "correctIndex": 3
        },
        {
          "id": "ent-q17",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out 4.8 × 10^5 ÷ (1.6 × 10^-2) on your calculator.",
          "data": {
            "family": "std-entry",
            "misconceptionDistractor": "3000",
            "misconceptionDistractors": [
              {
                "value": "768000",
                "code": "cu-e-notation",
                "feedback": "5.7E11 means 5.7 × 10¹¹ (standard form), not 5.7¹¹ and not 5.7 × 11."
              },
              {
                "value": "300000000",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "30000000",
          "difficulty": 2,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "Enter each standard-form number in one piece with ×10^x: 30000000.",
          "misconceptionCode": "cu-fraction-chain",
          "options": [
            "30000000",
            "3000",
            "768000",
            "300000000"
          ],
          "correctIndex": 0
        },
        {
          "id": "ent-q18",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out 2.7 × 10^4 ÷ (9 × 10^-3) on your calculator.",
          "data": {
            "family": "std-entry",
            "misconceptionDistractor": "30000000",
            "misconceptionDistractors": [
              {
                "value": "3",
                "code": "cu-fraction-chain",
                "feedback": "Chained division goes left to right: divide by the WHOLE denominator — brackets or the fraction key."
              },
              {
                "value": "243000",
                "code": "cu-e-notation",
                "feedback": "5.7E11 means 5.7 × 10¹¹ (standard form), not 5.7¹¹ and not 5.7 × 11."
              }
            ]
          },
          "correctAnswer": "3000000",
          "difficulty": 2,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "Enter each standard-form number in one piece with ×10^x: 3000000.",
          "misconceptionCode": "cu-arithmetic",
          "options": [
            "30000000",
            "3000000",
            "3",
            "243000"
          ],
          "correctIndex": 1
        },
        {
          "id": "ent-q19",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out 5.6 × 10^-2 ÷ (2 × 10^5) on your calculator.",
          "data": {
            "family": "std-entry",
            "misconceptionDistractor": "2800",
            "misconceptionDistractors": [
              {
                "value": "0.112",
                "code": "cu-e-notation",
                "feedback": "5.7E11 means 5.7 × 10¹¹ (standard form), not 5.7¹¹ and not 5.7 × 11."
              },
              {
                "value": "0.0000028",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "0.00000028",
          "difficulty": 3,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "Enter each standard-form number in one piece with ×10^x: 0.00000028.",
          "misconceptionCode": "cu-fraction-chain",
          "options": [
            "0.112",
            "2800",
            "0.00000028",
            "0.0000028"
          ],
          "correctIndex": 2
        },
        {
          "id": "ent-q20",
          "objectiveRecordIds": [
            "0580-core-C1.14-1",
            "0580-core-C1.14-2",
            "0580-extended-E1.14-1",
            "0580-extended-E1.14-2"
          ],
          "prompt": "Work out 8.1 × 10^7 ÷ (2.7 × 10^3) on your calculator.",
          "data": {
            "family": "std-entry",
            "misconceptionDistractor": "30000000000",
            "misconceptionDistractors": [
              {
                "value": "218700000",
                "code": "cu-e-notation",
                "feedback": "5.7E11 means 5.7 × 10¹¹ (standard form), not 5.7¹¹ and not 5.7 × 11."
              },
              {
                "value": "300000",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "30000",
          "difficulty": 3,
          "hint": "Plan the sequence before you press: brackets around every long numerator and denominator, the root and power keys cover only their bracket, (−) makes a negative base, and ×10^x enters standard form in one piece.",
          "explanation": "Enter each standard-form number in one piece with ×10^x: 30000.",
          "misconceptionCode": "cu-fraction-chain",
          "options": [
            "300000",
            "30000000000",
            "218700000",
            "30000"
          ],
          "correctIndex": 3
        }
      ]
    },
    "read-the-display": {
      "minimumDistinctItems": 19,
      "objectiveRecordIds": [
        "0580-core-C1.14-3",
        "0580-extended-E1.14-3"
      ],
      "items": [
        {
          "id": "rea-q01",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 5.7E11. What is this number?",
          "data": {
            "family": "e-notation",
            "misconceptionDistractor": "206358998.93",
            "misconceptionDistractors": [
              {
                "value": "62.7",
                "code": "cu-e-notation",
                "feedback": "5.7E11 means 5.7 × 10¹¹ (standard form), not 5.7¹¹ and not 5.7 × 11."
              },
              {
                "value": "5700000000000",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "570000000000",
          "difficulty": 1,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "E11 means × 10^11: 5.7E11 is 570000000000.",
          "misconceptionCode": "cu-e-notation",
          "options": [
            "570000000000",
            "206358998.93",
            "62.7",
            "5700000000000"
          ],
          "correctIndex": 0
        },
        {
          "id": "rea-q02",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 1.03E7. What is this number?",
          "data": {
            "family": "e-notation",
            "misconceptionDistractor": "103000000",
            "misconceptionDistractors": [
              {
                "value": "1.23",
                "code": "cu-e-notation",
                "feedback": "5.7E11 means 5.7 × 10¹¹ (standard form), not 5.7¹¹ and not 5.7 × 11."
              },
              {
                "value": "7.21",
                "code": "cu-e-notation",
                "feedback": "5.7E11 means 5.7 × 10¹¹ (standard form), not 5.7¹¹ and not 5.7 × 11."
              }
            ]
          },
          "correctAnswer": "10300000",
          "difficulty": 1,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "E7 means × 10^7: 1.03E7 is 10300000.",
          "misconceptionCode": "cu-arithmetic",
          "options": [
            "103000000",
            "10300000",
            "1.23",
            "7.21"
          ],
          "correctIndex": 1
        },
        {
          "id": "rea-q03",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 4.2E-5. What is this number?",
          "data": {
            "family": "e-notation",
            "misconceptionDistractor": "1306.91",
            "misconceptionDistractors": [
              {
                "value": "21",
                "code": "cu-e-notation",
                "feedback": "5.7E11 means 5.7 × 10¹¹ (standard form), not 5.7¹¹ and not 5.7 × 11."
              },
              {
                "value": "0.0000042",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "0.000042",
          "difficulty": 2,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "E-5 means × 10^-5: 4.2E-5 is 0.000042.",
          "misconceptionCode": "cu-e-notation",
          "options": [
            "21",
            "1306.91",
            "0.000042",
            "0.0000042"
          ],
          "correctIndex": 2
        },
        {
          "id": "rea-q04",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 9.99E12. What is this number?",
          "data": {
            "family": "e-notation",
            "misconceptionDistractor": "988065780494.21",
            "misconceptionDistractors": [
              {
                "value": "119.88",
                "code": "cu-e-notation",
                "feedback": "5.7E11 means 5.7 × 10¹¹ (standard form), not 5.7¹¹ and not 5.7 × 11."
              },
              {
                "value": "99900000000000",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "9990000000000",
          "difficulty": 2,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "E12 means × 10^12: 9.99E12 is 9990000000000.",
          "misconceptionCode": "cu-e-notation",
          "options": [
            "99900000000000",
            "988065780494.21",
            "119.88",
            "9990000000000"
          ],
          "correctIndex": 3
        },
        {
          "id": "rea-q05",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 6.5E4. What is this number?",
          "data": {
            "family": "e-notation",
            "misconceptionDistractor": "1785.06",
            "misconceptionDistractors": [
              {
                "value": "26",
                "code": "cu-e-notation",
                "feedback": "5.7E11 means 5.7 × 10¹¹ (standard form), not 5.7¹¹ and not 5.7 × 11."
              },
              {
                "value": "650000",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "65000",
          "difficulty": 1,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "E4 means × 10^4: 6.5E4 is 65000.",
          "misconceptionCode": "cu-e-notation",
          "options": [
            "65000",
            "1785.06",
            "26",
            "650000"
          ],
          "correctIndex": 0
        },
        {
          "id": "rea-q06",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 7/8 as a fraction. What is this number as a decimal?",
          "data": {
            "family": "fraction-display",
            "misconceptionDistractor": "7.8",
            "misconceptionDistractors": [
              {
                "value": "5.6",
                "code": "cu-fraction-display",
                "feedback": "That reads as a fraction — the calculator fraction mark means division, not a decimal point."
              },
              {
                "value": "1",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "0.875",
          "difficulty": 1,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "7/8 = 0.875: the fraction mark is a division.",
          "misconceptionCode": "cu-fraction-display",
          "options": [
            "7.8",
            "0.875",
            "5.6",
            "1"
          ],
          "correctIndex": 1
        },
        {
          "id": "rea-q07",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 11/20 as a fraction. What is this number as a decimal?",
          "data": {
            "family": "fraction-display",
            "misconceptionDistractor": "0.6",
            "misconceptionDistractors": [
              {
                "value": "11.2",
                "code": "cu-fraction-display",
                "feedback": "That reads as a fraction — the calculator fraction mark means division, not a decimal point."
              },
              {
                "value": "22",
                "code": "cu-fraction-display",
                "feedback": "That reads as a fraction — the calculator fraction mark means division, not a decimal point."
              }
            ]
          },
          "correctAnswer": "0.55",
          "difficulty": 1,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "11/20 = 0.55: the fraction mark is a division.",
          "misconceptionCode": "cu-arithmetic",
          "options": [
            "11.2",
            "0.6",
            "0.55",
            "22"
          ],
          "correctIndex": 2
        },
        {
          "id": "rea-q08",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 5/16 as a fraction. What is this number as a decimal?",
          "data": {
            "family": "fraction-display",
            "misconceptionDistractor": "5.16",
            "misconceptionDistractors": [
              {
                "value": "8",
                "code": "cu-fraction-display",
                "feedback": "That reads as a fraction — the calculator fraction mark means division, not a decimal point."
              },
              {
                "value": "0.375",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "0.3125",
          "difficulty": 2,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "5/16 = 0.3125: the fraction mark is a division.",
          "misconceptionCode": "cu-fraction-display",
          "options": [
            "0.375",
            "5.16",
            "8",
            "0.3125"
          ],
          "correctIndex": 3
        },
        {
          "id": "rea-q09",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 3/40 as a fraction. What is this number as a decimal?",
          "data": {
            "family": "fraction-display",
            "misconceptionDistractor": "3.4",
            "misconceptionDistractors": [
              {
                "value": "12",
                "code": "cu-fraction-display",
                "feedback": "That reads as a fraction — the calculator fraction mark means division, not a decimal point."
              },
              {
                "value": "0.1",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "0.075",
          "difficulty": 2,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "3/40 = 0.075: the fraction mark is a division.",
          "misconceptionCode": "cu-fraction-display",
          "options": [
            "0.075",
            "3.4",
            "12",
            "0.1"
          ],
          "correctIndex": 0
        },
        {
          "id": "rea-q10",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 9/25 as a fraction. What is this number as a decimal?",
          "data": {
            "family": "fraction-display",
            "misconceptionDistractor": "9.25",
            "misconceptionDistractors": [
              {
                "value": "22.5",
                "code": "cu-fraction-display",
                "feedback": "That reads as a fraction — the calculator fraction mark means division, not a decimal point."
              },
              {
                "value": "0.4",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "0.36",
          "difficulty": 3,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "9/25 = 0.36: the fraction mark is a division.",
          "misconceptionCode": "cu-fraction-display",
          "options": [
            "9.25",
            "0.36",
            "22.5",
            "0.4"
          ],
          "correctIndex": 1
        },
        {
          "id": "rea-q11",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 3 1/4 as a mixed fraction. What is this number as a decimal?",
          "data": {
            "family": "mixed-display",
            "misconceptionDistractor": "0.75",
            "misconceptionDistractors": [
              {
                "value": "3.1",
                "code": "cu-fraction-display",
                "feedback": "That reads as a fraction — the calculator fraction mark means division, not a decimal point."
              },
              {
                "value": "4.25",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "3.25",
          "difficulty": 2,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "3 1/4 is 3 + 1/4 = 3.25.",
          "misconceptionCode": "cu-fraction-display",
          "options": [
            "3.1",
            "0.75",
            "3.25",
            "4.25"
          ],
          "correctIndex": 2
        },
        {
          "id": "rea-q12",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 1 2/5 as a mixed fraction. What is this number as a decimal?",
          "data": {
            "family": "mixed-display",
            "misconceptionDistractor": "0.4",
            "misconceptionDistractors": [
              {
                "value": "1.2",
                "code": "cu-fraction-display",
                "feedback": "That reads as a fraction — the calculator fraction mark means division, not a decimal point."
              },
              {
                "value": "2.4",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "1.4",
          "difficulty": 1,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "1 2/5 is 1 + 2/5 = 1.4.",
          "misconceptionCode": "cu-fraction-display",
          "options": [
            "2.4",
            "0.4",
            "1.2",
            "1.4"
          ],
          "correctIndex": 3
        },
        {
          "id": "rea-q13",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 2 3/8 as a mixed fraction. What is this number as a decimal?",
          "data": {
            "family": "mixed-display",
            "misconceptionDistractor": "3.375",
            "misconceptionDistractors": [
              {
                "value": "0.75",
                "code": "cu-fraction-display",
                "feedback": "That reads as a fraction — the calculator fraction mark means division, not a decimal point."
              },
              {
                "value": "2.3",
                "code": "cu-fraction-display",
                "feedback": "That reads as a fraction — the calculator fraction mark means division, not a decimal point."
              }
            ]
          },
          "correctAnswer": "2.375",
          "difficulty": 2,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "2 3/8 is 2 + 3/8 = 2.375.",
          "misconceptionCode": "cu-arithmetic",
          "options": [
            "2.375",
            "3.375",
            "0.75",
            "2.3"
          ],
          "correctIndex": 0
        },
        {
          "id": "rea-q14",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 4 1/2 as a mixed fraction. What is this number as a decimal?",
          "data": {
            "family": "mixed-display",
            "misconceptionDistractor": "2",
            "misconceptionDistractors": [
              {
                "value": "4.1",
                "code": "cu-fraction-display",
                "feedback": "That reads as a fraction — the calculator fraction mark means division, not a decimal point."
              },
              {
                "value": "5.5",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "4.5",
          "difficulty": 1,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "4 1/2 is 4 + 1/2 = 4.5.",
          "misconceptionCode": "cu-fraction-display",
          "options": [
            "2",
            "4.5",
            "4.1",
            "5.5"
          ],
          "correctIndex": 1
        },
        {
          "id": "rea-q15",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 0.070463. Round the value to 3 significant figures.",
          "data": {
            "family": "rounding",
            "misconceptionDistractor": "0.0704",
            "misconceptionDistractors": [
              {
                "value": "0.070",
                "code": "cu-rounding",
                "feedback": "Round the FINAL display to the accuracy asked: count significant figures from the first non-zero digit, and look at the next digit."
              },
              {
                "value": "0.705",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "0.0705",
          "difficulty": 2,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "0.070463 to 3 significant figures is 0.0705 (count from the first non-zero digit).",
          "misconceptionCode": "cu-rounding",
          "options": [
            "0.070",
            "0.0704",
            "0.0705",
            "0.705"
          ],
          "correctIndex": 2
        },
        {
          "id": "rea-q16",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 45.2718. Round the value to 3 significant figures.",
          "data": {
            "family": "rounding",
            "misconceptionDistractor": "45.2",
            "misconceptionDistractors": [
              {
                "value": "45.272",
                "code": "cu-rounding",
                "feedback": "Round the FINAL display to the accuracy asked: count significant figures from the first non-zero digit, and look at the next digit."
              },
              {
                "value": "453",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "45.3",
          "difficulty": 1,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "45.2718 to 3 significant figures is 45.3 (count from the first non-zero digit).",
          "misconceptionCode": "cu-rounding",
          "options": [
            "453",
            "45.2",
            "45.272",
            "45.3"
          ],
          "correctIndex": 3
        },
        {
          "id": "rea-q17",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 0.0056234. Round the value to 2 significant figures.",
          "data": {
            "family": "rounding",
            "misconceptionDistractor": "0.056",
            "misconceptionDistractors": [
              {
                "value": "0.00562",
                "code": "cu-rounding",
                "feedback": "Round the FINAL display to the accuracy asked: count significant figures from the first non-zero digit, and look at the next digit."
              },
              {
                "value": "0.006",
                "code": "cu-rounding",
                "feedback": "Round the FINAL display to the accuracy asked: count significant figures from the first non-zero digit, and look at the next digit."
              }
            ]
          },
          "correctAnswer": "0.0056",
          "difficulty": 2,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "0.0056234 to 2 significant figures is 0.0056 (count from the first non-zero digit).",
          "misconceptionCode": "cu-arithmetic",
          "options": [
            "0.0056",
            "0.056",
            "0.00562",
            "0.006"
          ],
          "correctIndex": 0
        },
        {
          "id": "rea-q18",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows 7.6555. Round the value to 4 significant figures.",
          "data": {
            "family": "rounding",
            "misconceptionDistractor": "7.655",
            "misconceptionDistractors": [
              {
                "value": "7.6555",
                "code": "cu-rounding",
                "feedback": "Round the FINAL display to the accuracy asked: count significant figures from the first non-zero digit, and look at the next digit."
              },
              {
                "value": "76.56",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "7.656",
          "difficulty": 3,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "7.6555 to 4 significant figures is 7.656 (count from the first non-zero digit).",
          "misconceptionCode": "cu-rounding",
          "options": [
            "7.655",
            "7.656",
            "7.6555",
            "76.56"
          ],
          "correctIndex": 1
        },
        {
          "id": "rea-q19",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows −2.5E-4. What is this number?",
          "data": {
            "family": "negative-e",
            "misconceptionDistractor": "0.00025",
            "misconceptionDistractors": [
              {
                "value": "-0.000025",
                "code": "cu-e-notation",
                "feedback": "5.7E11 means 5.7 × 10¹¹ (standard form), not 5.7¹¹ and not 5.7 × 11."
              },
              {
                "value": "-0.0025",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "-0.00025",
          "difficulty": 3,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "−2.5E-4 is −2.5 × 10^-4 = -0.00025 — keep the sign.",
          "misconceptionCode": "cu-sign-lost",
          "options": [
            "-0.000025",
            "0.00025",
            "-0.00025",
            "-0.0025"
          ],
          "correctIndex": 2
        },
        {
          "id": "rea-q20",
          "objectiveRecordIds": [
            "0580-core-C1.14-3",
            "0580-extended-E1.14-3"
          ],
          "prompt": "The calculator display shows −1.6E6. What is this number?",
          "data": {
            "family": "negative-e",
            "misconceptionDistractor": "1600000",
            "misconceptionDistractors": [
              {
                "value": "-160000",
                "code": "cu-e-notation",
                "feedback": "5.7E11 means 5.7 × 10¹¹ (standard form), not 5.7¹¹ and not 5.7 × 11."
              },
              {
                "value": "-16000000",
                "code": "cu-arithmetic",
                "feedback": "The method is right; check the key presses — digits and signs, kept exact."
              }
            ]
          },
          "correctAnswer": "-1600000",
          "difficulty": 2,
          "hint": "Read the display as mathematics: E11 means × 10¹¹, a stacked mark is a fraction bar (5 over 16 is 5/16), and a mixed display shows a + b/c. Round only at the end, counting significant figures from the first non-zero digit.",
          "explanation": "−1.6E6 is −1.6 × 10^6 = -1600000 — keep the sign.",
          "misconceptionCode": "cu-sign-lost",
          "options": [
            "-16000000",
            "1600000",
            "-160000",
            "-1600000"
          ],
          "correctIndex": 3
        }
      ]
    }
  }
}