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Rational to Decimal

Grade 7 · Decimals · Worksheet 1

  1. 0.375 × 2.8 ÷ 0.7 = ? Answer: ______________
  2. A square garden is drawn on a coordinate plane with vertices at (0, 0), (21, 0), (21, 21), and (0, 21). Inside the garden, a circular flower bed is centered at (11, 11) with a radius of 6 units. What is the area of the garden that is not covered by the flower bed? Use 3.14 for π.
    Answer: ______________
  3. 0.75 × 1.2 ÷ 0.5 = ? Answer: ______________
  4. Isabella is helping her grandmother make traditional fruit preserves. The recipe calls for 0.83̄ (repeating 3) cups of sugar for every batch. If Isabella wants to make 9 batches of preserves, how many total cups of sugar will she need? Express your answer as a decimal. Answer: ______________
  5. A large rectangular garden is drawn on a coordinate plane with vertices at (0, 0), (42, 0), (42, 24), and (0, 24). A circular fountain is placed in the center of the garden, with its center at (21, 12) and a radius of 7 units. What is the area of the garden that is planted with grass (excluding the fountain)? Use π = 22/7. Answer: ______________
  6. Mason is designing a mosaic on a coordinate grid. The mosaic features a large rectangle with vertices at (0, 0), (77, 0), (77, 42), and (0, 42). Inside this rectangle, he draws a diagonal line from (0, 0) to (77, 42). He then colors the region below this diagonal line. What fraction of the rectangle's area is colored? Express your answer as a simplified fraction and as a repeating decimal (use bar notation for the repeating part). Answer: ______________
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Answer Key & Explanations

Rational to Decimal · Grade 7 · Worksheet 1

  1. 0.375 × 2.8 ÷ 0.7 = ? Answer: 1.5 Solution: Convert 0.375 to a fraction: 0.375 = 375/1000 = 3/8 Write the expression as (3/8) × 2.8 ÷ 0.7 Convert 2.8 to a fraction: 2.8 = 28/10 = 14/5 Convert 0.7 to a fraction: 0.7 = 7/10 Rewrite the expression: (3/8) × (14/5) ÷ (7/10) Division by a fraction is multiplication by its reciprocal: (3/8) ×…
    Full step-by-step solution

    Step 1: Convert 0.375 to a fraction: 0.375 = 375/1000 = 3/8 Step 2: Write the expression as (3/8) × 2.8 ÷ 0.7 Step 3: Convert 2.8 to a fraction: 2.8 = 28/10 = 14/5 Step 4: Convert 0.7 to a fraction: 0.7 = 7/10 Step 5: Rewrite the expression: (3/8) × (14/5) ÷ (7/10) Step 6: Division by a fraction is multiplication by its reciprocal: (3/8) × (14/5) × (10/7) Step 7: Multiply numerators: 3 × 14 × 10 = 420 Step 8: Multiply denominators: 8 × 5 × 7 = 280 Step 9: Simplify the fraction: 420/280 = 42/28 = 21/14 = 3/2 = 1.5 Step 10: The answer is 1.5

  2. A square garden is drawn on a coordinate plane with vertices at (0, 0), (21, 0), (21, 21), and (0, 21). Inside the garden, a circular flower bed is centered at (11, 11) with a radius of 6 units. What is the area of the garden that is not covered by the flower bed? Use 3.14 for π. Answer: 327.96 Solution: Find the area of the square garden. Side length = 21 units. Area = side × side = 21 × 21 = 441 square units.
    Full step-by-step solution

    Step 1: Find the area of the square garden. Side length = 21 units. Area = side × side = 21 × 21 = 441 square units. Step 2: Find the area of the circular flower bed. Radius = 6 units. Area = π × r² = 3.14 × 6 × 6 = 3.14 × 36 = 113.04 square units. Step 3: Subtract the area of the flower bed from the total garden area. Area uncovered = 441 - 113.04 = 327.96 square units. The answer is 327.96.

  3. 0.75 × 1.2 ÷ 0.5 = ? Answer: 1.8 Solution: Write the problem clearly. 0.75 × 1.2 ÷ 0.5 Multiplication and division have the same priority, so we go left to right. First, multiply 0.75 × 1.2.
    Full step-by-step solution

    Let's solve step by step. Step 1: Write the problem clearly. 0.75 × 1.2 ÷ 0.5 Step 2: Multiplication and division have the same priority, so we go left to right. First, multiply 0.75 × 1.2. 0.75 × 1.2 = 0.75 × (12/10) = (75/100) × (12/10) = (75 × 12) / (100 × 10) = 900 / 1000 = 0.9 So after the first step: 0.9 ÷ 0.5 Step 3: Now divide 0.9 ÷ 0.5. 0.9 ÷ 0.5 = 0.9 / 0.5 = (9/10) / (5/10) = (9/10) × (10/5) = 9/5 = 1.8 Step 4: Final answer. 0.75 × 1.2 ÷ 0.5 = 1.8

  4. Isabella is helping her grandmother make traditional fruit preserves. The recipe calls for 0.83̄ (repeating 3) cups of sugar for every batch. If Isabella wants to make 9 batches of preserves, how many total cups of sugar will she need? Express your answer as a decimal. Answer: 7.5 Solution: Convert 0.83̄ (repeating 3) to a fraction. Let x = 0.8333... Multiply both sides by 10: 10x = 8.333...
    Full step-by-step solution

    Step 1: Convert 0.83̄ (repeating 3) to a fraction. Let x = 0.8333... Multiply both sides by 10: 10x = 8.333... Subtract the original equation: 10x - x = 8.333... - 0.833... → 9x = 7.5 → x = 7.5/9 = 75/90 = 5/6. Step 2: Multiply by 9 batches: (5/6) × 9 = (5 × 9)/6 = 45/6 = 15/2 = 7.5 cups. The answer is 7.5 cups of sugar.

  5. A large rectangular garden is drawn on a coordinate plane with vertices at (0, 0), (42, 0), (42, 24), and (0, 24). A circular fountain is placed in the center of the garden, with its center at (21, 12) and a radius of 7 units. What is the area of the garden that is planted with grass (excluding the fountain)? Use π = 22/7. Answer: 854 Solution: Find the area of the rectangular garden. Length = 42 units (from x=0 to x=42), Width = 24 units (from y=0 to y=24). Area = length × width = 42 × 24 = 1008 square units.
    Full step-by-step solution

    Step 1: Find the area of the rectangular garden. Length = 42 units (from x=0 to x=42), Width = 24 units (from y=0 to y=24). Area = length × width = 42 × 24 = 1008 square units. Step 2: Find the area of the circular fountain. Radius = 7 units. Using π = 22/7, Area = π × r^2 = (22/7) × 7^2 = (22/7) × 49 = 22 × 7 = 154 square units. Step 3: Subtract the fountain area from the garden area to get the grass area. Grass area = 1008 - 154 = 854 square units. The answer is 854.

  6. Mason is designing a mosaic on a coordinate grid. The mosaic features a large rectangle with vertices at (0, 0), (77, 0), (77, 42), and (0, 42). Inside this rectangle, he draws a diagonal line from (0, 0) to (77, 42). He then colors the region below this diagonal line. What fraction of the rectangle's area is colored? Express your answer as a simplified fraction and as a repeating decimal (use bar notation for the repeating part). Answer: Fraction: 1/2, Decimal: 0.5 Solution: Find the area of the rectangle. The rectangle has length 77 units and width 42 units. Area = length × width = 77 × 42 = 3234 square units.
    Full step-by-step solution

    Step 1: Find the area of the rectangle. The rectangle has length 77 units and width 42 units. Area = length × width = 77 × 42 = 3234 square units. Step 2: Identify the shape below the diagonal. The diagonal line from (0, 0) to (77, 42) divides the rectangle into two triangles. The region below the diagonal is a triangle with base 77 units (along the x-axis) and height 42 units (vertical distance from the x-axis to the top-right corner at y=42). Step 3: Calculate the area of the triangle. Area of a triangle = (1/2) × base × height = (1/2) × 77 × 42 = (1/2) × 3234 = 1617 square units. Step 4: Find the fraction of the rectangle that is colored. Fraction = (area of triangle) / (area of rectangle) = 1617 / 3234. Simplify the fraction: 1617 ÷ 1617 = 1, and 3234 ÷ 1617 = 2. So the simplified fraction is 1/2. Step 5: Convert 1/2 to a decimal. 1/2 = 0.5. This is a terminating decimal, not a repeating one, so it can be written as 0.5 (no bar needed, as 0.5 has no repeating cycle). The answer is Fraction: 1/2, Decimal: 0.5.