{
  "Id": "fed9ac66-9966-47a4-9d66-8b805e69a39a",
  "Title": "Advanced Decimals: Place Value, Operations, and Applications",
  "Subject": "Mathematics",
  "Topic": "Decimals \u2014 place value, number line, operations, conversions, and real-life applications",
  "Instructions": "Read each question carefully and answer to the best of your ability. Show all working for word problems.",
  "EstimatedMinutes": 35,
  "StudentProfileId": "dd186faa-f489-46ee-84e4-26e2d01e2691",
  "SourceFileName": "decimal.pdf",
  "SessionMaterialId": "e519f06f-7536-46b1-a7f4-e243ea85ea17",
  "GeneratedAt": "2026-07-25T12:20:44.733367Z",
  "Questions": [
    {
      "Id": 1,
      "Type": "word_problem",
      "Text": "A jacket marked at $48.75 is sold with a 15% discount, and then an 8% sales tax is applied to the discounted price. What is the final price to the nearest cent?",
      "Options": [],
      "Answer": "Step 1: Discount = 48.75 \u00D7 0.15 = 7.3125\nStep 2: Discounted price = 48.75 \u2212 7.3125 = 41.4375\nStep 3: Tax = 41.4375 \u00D7 0.08 = 3.315\nStep 4: Final price = 41.4375 \u002B 3.315 = 44.7525\nAnswer: $44.75",
      "Points": 3
    },
    {
      "Id": 2,
      "Type": "word_problem",
      "Text": "A 12.6 m rope is cut into three pieces. Two pieces measure 2.75 m and 4.8 m. The remaining rope is used to make two ties of 0.95 m each. How many meters of rope are left unused?",
      "Options": [],
      "Answer": "Step 1: Sum of first two pieces = 2.75 \u002B 4.8 = 7.55 m\nStep 2: Rope after two pieces = 12.6 \u2212 7.55 = 5.05 m\nStep 3: Rope used for ties = 2 \u00D7 0.95 = 1.90 m\nStep 4: Leftover = 5.05 \u2212 1.90 = 3.15 m\nAnswer: 3.15 m",
      "Points": 3
    },
    {
      "Id": 3,
      "Type": "word_problem",
      "Text": "Two bottles contain 1.25 L and 0.85 L of juice. They are poured into a carafe that can hold 1.90 L. How much overflows?",
      "Options": [],
      "Answer": "Step 1: Total juice = 1.25 \u002B 0.85 = 2.10 L\nStep 2: Overflow = 2.10 \u2212 1.90 = 0.20 L\nAnswer: 0.20 L",
      "Points": 3
    },
    {
      "Id": 4,
      "Type": "word_problem",
      "Text": "A runner\u2019s lap times (in minutes) are 1.28, 1.31, 1.27, and 1.35. What is the average time, and by how many seconds does it differ from a target average of 1.30 minutes?",
      "Options": [],
      "Answer": "Step 1: Sum = 1.28 \u002B 1.31 \u002B 1.27 \u002B 1.35 = 5.21 min\nStep 2: Average = 5.21 \u00F7 4 = 1.3025 min\nStep 3: Difference from 1.30 = 1.3025 \u2212 1.30 = 0.0025 min\nStep 4: Convert to seconds = 0.0025 \u00D7 60 = 0.15 s\nAnswer: Average = 1.3025 min; Difference = 0.15 s above target",
      "Points": 3
    },
    {
      "Id": 5,
      "Type": "word_problem",
      "Text": "On a number line, A = 2.45 and B = 7.08. Point P is 1.75 units to the right of A. Find the coordinate of P and the distance from P to B.",
      "Options": [],
      "Answer": "Step 1: P = 2.45 \u002B 1.75 = 4.20\nStep 2: Distance PB = 7.08 \u2212 4.20 = 2.88\nAnswer: P = 4.20; Distance PB = 2.88",
      "Points": 3
    },
    {
      "Id": 6,
      "Type": "word_problem",
      "Text": "A measurement rounds to 5.62 when rounded to the nearest hundredth. State the minimum possible value, the maximum possible value (upper bound), and the width of this interval.",
      "Options": [],
      "Answer": "Step 1: For nearest hundredth, bounds are [5.615, 5.625)\nStep 2: Minimum = 5.615; Maximum (upper bound) = 5.625 (not included)\nStep 3: Width = 5.625 \u2212 5.615 = 0.010\nAnswer: Min = 5.615; Max \u003C 5.625; Interval width = 0.01",
      "Points": 3
    },
    {
      "Id": 7,
      "Type": "word_problem",
      "Text": "A shopper buys 3.5 kg of apples at $2.39 per kg and 1.8 kg of bananas at $1.75 per kg, paying with a $20 bill. Round only the final change to the nearest cent. How much change is received?",
      "Options": [],
      "Answer": "Step 1: Apple cost = 3.5 \u00D7 2.39 = 8.365\nStep 2: Banana cost = 1.8 \u00D7 1.75 = 3.15\nStep 3: Total cost = 8.365 \u002B 3.15 = 11.515\nStep 4: Change (unrounded) = 20.00 \u2212 11.515 = 8.485\nStep 5: Round change to nearest cent = $8.49\nAnswer: $8.49",
      "Points": 3
    },
    {
      "Id": 8,
      "Type": "word_problem",
      "Text": "A cyclist travels at 52.5 km/h for 1.6 hours and then at 48.3 km/h for 0.75 hours. What total distance does the cyclist cover?",
      "Options": [],
      "Answer": "Step 1: Distance 1 = 52.5 \u00D7 1.6 = 84.0 km\nStep 2: Distance 2 = 48.3 \u00D7 0.75 = 36.225 km\nStep 3: Total distance = 84.0 \u002B 36.225 = 120.225 km\nAnswer: 120.225 km",
      "Points": 3
    },
    {
      "Id": 9,
      "Type": "word_problem",
      "Text": "A rectangular garden is 8.4 m by 3.75 m. A uniform border of width 0.15 m is added around it. What is the area of the border?",
      "Options": [],
      "Answer": "Step 1: Inner area = 8.4 \u00D7 3.75 = 31.5 m\u00B2\nStep 2: Outer dimensions = (8.4 \u002B 2\u00D70.15) by (3.75 \u002B 2\u00D70.15) = 8.7 by 4.05\nStep 3: Outer area = 8.7 \u00D7 4.05 = 35.235 m\u00B2\nStep 4: Border area = 35.235 \u2212 31.5 = 3.735 m\u00B2\nAnswer: 3.735 m\u00B2",
      "Points": 3
    },
    {
      "Id": 10,
      "Type": "word_problem",
      "Text": "The sum of three decimal numbers is 23.57. Two of them are 8.946 and 7.800. Find the third number.",
      "Options": [],
      "Answer": "Step 1: Sum of known numbers = 8.946 \u002B 7.800 = 16.746\nStep 2: Third number = 23.57 \u2212 16.746 = 6.824\nAnswer: 6.824",
      "Points": 3
    },
    {
      "Id": 11,
      "Type": "word_problem",
      "Text": "A solution is made by mixing 0.50 L of 2.4% salt solution and 0.80 L of 1.5% salt solution. Assuming 1 L = 1000 g of solution, how many grams of salt are in the mixture?",
      "Options": [],
      "Answer": "Step 1: Mass in first portion = 0.50 L \u00D7 1000 g/L = 500 g; salt = 500 \u00D7 0.024 = 12 g\nStep 2: Mass in second portion = 0.80 L \u00D7 1000 g/L = 800 g; salt = 800 \u00D7 0.015 = 12 g\nStep 3: Total salt = 12 \u002B 12 = 24 g\nAnswer: 24 g",
      "Points": 3
    },
    {
      "Id": 12,
      "Type": "word_problem",
      "Text": "A car uses 3.6 L of fuel to travel 45.0 km and 2.9 L to travel another 38.0 km. What is the overall fuel consumption in L/100 km (rounded to two decimal places)?",
      "Options": [],
      "Answer": "Step 1: Total fuel = 3.6 \u002B 2.9 = 6.5 L\nStep 2: Total distance = 45.0 \u002B 38.0 = 83.0 km\nStep 3: L/100 km = (6.5 \u00F7 83.0) \u00D7 100 = 7.831325...\nStep 4: Round to two decimals = 7.83 L/100 km\nAnswer: 7.83 L/100 km",
      "Points": 3
    },
    {
      "Id": 13,
      "Type": "word_problem",
      "Text": "Solve for x: 3(1.2x \u2212 0.45) = 2.7 \u002B 0.9x.",
      "Options": [],
      "Answer": "Step 1: Expand left: 3 \u00D7 1.2x = 3.6x; 3 \u00D7 (\u22120.45) = \u22121.35\nStep 2: Equation: 3.6x \u2212 1.35 = 2.7 \u002B 0.9x\nStep 3: Subtract 0.9x: 2.7x \u2212 1.35 = 2.7\nStep 4: Add 1.35: 2.7x = 4.05\nStep 5: Divide: x = 4.05 \u00F7 2.7 = 1.5\nAnswer: x = 1.5",
      "Points": 3
    },
    {
      "Id": 14,
      "Type": "word_problem",
      "Text": "An arithmetic sequence starts at 0.85 and increases by 0.35 each term. What is the sum of the first 10 terms?",
      "Options": [],
      "Answer": "Step 1: a1 = 0.85, d = 0.35, n = 10\nStep 2: Sum formula: S_n = n/2 [2a1 \u002B (n\u22121)d]\nStep 3: S_10 = 10/2 [2(0.85) \u002B 9(0.35)] = 5[1.7 \u002B 3.15] = 5 \u00D7 4.85\nStep 4: Compute: 5 \u00D7 4.85 = 24.25\nAnswer: 24.25",
      "Points": 3
    },
    {
      "Id": 15,
      "Type": "word_problem",
      "Text": "A taxi charges a base fee of $3.50, $1.75 per km for the first 5 km, and $1.20 per km thereafter. How much does a 12.6 km ride cost?",
      "Options": [],
      "Answer": "Step 1: First 5 km cost = 5 \u00D7 1.75 = 8.75\nStep 2: Remaining distance = 12.6 \u2212 5 = 7.6 km\nStep 3: Remaining cost = 7.6 \u00D7 1.20 = 9.12\nStep 4: Total fare = 3.50 \u002B 8.75 \u002B 9.12 = 21.37\nAnswer: $21.37",
      "Points": 3
    },
    {
      "Id": 16,
      "Type": "word_problem",
      "Text": "A recipe uses 0.75 kg of flour to make 12 cookies. How many kilograms and grams of flour are needed to make 30 cookies?",
      "Options": [],
      "Answer": "Step 1: Scale factor = 30 \u00F7 12 = 2.5\nStep 2: Flour needed (kg) = 0.75 \u00D7 2.5 = 1.875 kg\nStep 3: Convert to grams = 1.875 \u00D7 1000 = 1875 g\nAnswer: 1.875 kg (which is 1875 g)",
      "Points": 3
    },
    {
      "Id": 17,
      "Type": "word_problem",
      "Text": "A worker logged 7.6 h on Monday, 8.25 h on Tuesday, and 6.9 h on Wednesday. To average at least 8.0 h per day over a 5-day week, how many total hours must be worked on Thursday and Friday combined?",
      "Options": [],
      "Answer": "Step 1: Required total = 5 \u00D7 8.0 = 40.0 h\nStep 2: Hours so far = 7.6 \u002B 8.25 \u002B 6.9 = 22.75 h\nStep 3: Needed Thu\u002BFri = 40.0 \u2212 22.75 = 17.25 h\nAnswer: 17.25 h",
      "Points": 3
    },
    {
      "Id": 18,
      "Type": "word_problem",
      "Text": "A stock rises from $12.48 to $14.10. What is the percent increase, rounded to two decimal places?",
      "Options": [],
      "Answer": "Step 1: Increase = 14.10 \u2212 12.48 = 1.62\nStep 2: Percent increase = (1.62 \u00F7 12.48) \u00D7 100 = 12.980769...\nStep 3: Round to two decimals = 12.98%\nAnswer: 12.98%",
      "Points": 3
    },
    {
      "Id": 19,
      "Type": "word_problem",
      "Text": "A bucket holds 12.5 L of water. A leak drips at a constant rate of 0.075 L per minute into the bucket. How long will it take to collect 3/5 of the bucket\u2019s capacity?",
      "Options": [],
      "Answer": "Step 1: Target volume = (3/5) \u00D7 12.5 = 7.5 L\nStep 2: Time = 7.5 \u00F7 0.075 = 100 minutes\nAnswer: 100 minutes",
      "Points": 3
    },
    {
      "Id": 20,
      "Type": "word_problem",
      "Text": "Two phone plans are compared for 42 calls: Plan A charges $19.95 per month plus $0.35 per call; Plan B charges a flat $31.50. Which plan is cheaper and by how much?",
      "Options": [],
      "Answer": "Step 1: Plan A variable = 0.35 \u00D7 42 = 14.70\nStep 2: Plan A total = 19.95 \u002B 14.70 = 34.65\nStep 3: Plan B total = 31.50\nStep 4: Difference = 34.65 \u2212 31.50 = 3.15\nAnswer: Plan B is cheaper by $3.15",
      "Points": 3
    },
    {
      "Id": 21,
      "Type": "fill_blank",
      "Text": "Compute (4.2 \u002B 0.86) \u2212 1.375 = _____",
      "Options": [],
      "Answer": "3.685",
      "Points": 3
    },
    {
      "Id": 22,
      "Type": "fill_blank",
      "Text": "7.5 \u00F7 0.12, rounded to the nearest tenth, equals _____",
      "Options": [],
      "Answer": "62.5",
      "Points": 3
    },
    {
      "Id": 23,
      "Type": "fill_blank",
      "Text": "The digit d that makes 7.d89 round to 7.9 (nearest tenth) and 7.89 (nearest hundredth) is _____",
      "Options": [],
      "Answer": "8",
      "Points": 3
    },
    {
      "Id": 24,
      "Type": "fill_blank",
      "Text": "Solve for x: 0.4x \u002B 1.27 = 3.03 \u21D2 x = _____",
      "Options": [],
      "Answer": "4.4",
      "Points": 3
    },
    {
      "Id": 25,
      "Type": "fill_blank",
      "Text": "The combined mass of 0.845 kg, 0.915 kg, and 1.075 kg is _____ kg",
      "Options": [],
      "Answer": "2.835",
      "Points": 3
    },
    {
      "Id": 26,
      "Type": "fill_blank",
      "Text": "Write 17/40 as a decimal: _____",
      "Options": [],
      "Answer": "0.425",
      "Points": 3
    },
    {
      "Id": 27,
      "Type": "fill_blank",
      "Text": "Complete: 2.4 \u002B _____ = 3(1.05)",
      "Options": [],
      "Answer": "0.75",
      "Points": 3
    },
    {
      "Id": 28,
      "Type": "fill_blank",
      "Text": "Evaluate 0.048 \u00D7 125 = _____",
      "Options": [],
      "Answer": "6",
      "Points": 3
    },
    {
      "Id": 29,
      "Type": "fill_blank",
      "Text": "If y = 1.2x and x = 0.35, then y = _____",
      "Options": [],
      "Answer": "0.42",
      "Points": 3
    },
    {
      "Id": 30,
      "Type": "fill_blank",
      "Text": "The mean of 5.84, 6.12, and 6.74 rounded to the nearest hundredth is _____",
      "Options": [],
      "Answer": "6.23",
      "Points": 3
    },
    {
      "Id": 31,
      "Type": "fill_blank",
      "Text": "The number that satisfies 0.25 \u00D7 _____ = 3.75 is _____",
      "Options": [],
      "Answer": "15",
      "Points": 3
    },
    {
      "Id": 32,
      "Type": "fill_blank",
      "Text": "Round 8.945 to the nearest hundredth: _____",
      "Options": [],
      "Answer": "8.95",
      "Points": 3
    },
    {
      "Id": 33,
      "Type": "fill_blank",
      "Text": "Compute 9.8 \u00F7 0.02 = _____",
      "Options": [],
      "Answer": "490",
      "Points": 3
    },
    {
      "Id": 34,
      "Type": "fill_blank",
      "Text": "With exactly three decimal places, the least number that rounds to 2.31 (nearest hundredth) is _____",
      "Options": [],
      "Answer": "2.305",
      "Points": 3
    },
    {
      "Id": 35,
      "Type": "fill_blank",
      "Text": "Find t: 6.4 \u002B t = 2.5 \u00D7 3.2 \u21D2 t = _____",
      "Options": [],
      "Answer": "1.6",
      "Points": 3
    },
    {
      "Id": 36,
      "Type": "fill_blank",
      "Text": "Convert 3 km 45 m to kilometers as a decimal: _____ km",
      "Options": [],
      "Answer": "3.045",
      "Points": 3
    },
    {
      "Id": 37,
      "Type": "fill_blank",
      "Text": "A rectangle\u2019s area is 12.96 m\u00B2 and one side is 3.2 m. The other side is _____ m",
      "Options": [],
      "Answer": "4.05",
      "Points": 3
    },
    {
      "Id": 38,
      "Type": "fill_blank",
      "Text": "Decrease 5.2 by 15%: _____",
      "Options": [],
      "Answer": "4.42",
      "Points": 3
    },
    {
      "Id": 39,
      "Type": "fill_blank",
      "Text": "Let p = 0.36 \u00D7 2.5. Then p \u002B 1.04 = _____",
      "Options": [],
      "Answer": "1.94",
      "Points": 3
    },
    {
      "Id": 40,
      "Type": "fill_blank",
      "Text": "Complete the equation: 7.203 \u002B _____ = 10.5",
      "Options": [],
      "Answer": "3.297",
      "Points": 3
    }
  ],
  "TotalPoints": 120
}