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Rational to Decimal

Grade 7 · Decimals · Worksheet 3

  1. Aroha is designing a large geometric pattern on a coordinate grid. She draws a rectangle with vertices at (0, 0), (36, 0), (36, 24), and (0, 24). Inside the rectangle, she draws a diagonal line from (0, 0) to (36, 24). She then shades the triangular region below this diagonal. What fraction of the rectangle's area is shaded? Express your answer as a decimal. Answer: ______________
  2. Olivia is designing a mosaic pattern on a coordinate grid. She draws a large square with vertices at (0, 0), (15, 0), (15, 15), and (0, 15). Inside this square, she marks a smaller square with vertices at (3, 3), (12, 3), (12, 12), and (3, 12). What fraction of the area of the large square is the area of the smaller square? Express your answer as a decimal. Answer: ______________
  3. Mason is building a model of a Ferris wheel for a school project. The plans indicate that the circumference of the wheel is 7/9 of the total height of the structure. Mason needs to convert this fraction to a decimal to program a motor controller. What is 7/9 written as a repeating decimal? Use a bar over the repeating digit(s). Answer: ______________
  4. Mason is helping his uncle build a custom bookshelf. The plans specify that each shelf support must be cut to a length of 2/7 of a meter. Mason's tape measure only shows decimal markings, so he needs to convert this fraction to a decimal to make an accurate cut. What is the decimal equivalent of 2/7? Express your answer as a repeating decimal using a bar over the repeating part. Answer: ______________
  5. 0.375 × 2.4 ÷ 0.5 = ? Answer: ______________
  6. Mason is helping his grandmother create a custom birdseed mixture. The recipe calls for 5/11 of the total mixture to be sunflower seeds. Mason needs to make 16.5 kilograms of birdseed. How many kilograms of sunflower seeds does he need? Express your answer as a decimal. Answer: ______________
  7. Emma is conducting a science experiment to create a special plant fertilizer solution. She needs to mix 2.25 liters of concentrated nutrient liquid with water to make a total of 15 liters of usable fertilizer. What fraction of the final solution is the concentrated nutrient liquid? Express your answer as a simplified fraction. Answer: ______________
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Answer Key & Explanations

Rational to Decimal · Grade 7 · Worksheet 3

  1. Aroha is designing a large geometric pattern on a coordinate grid. She draws a rectangle with vertices at (0, 0), (36, 0), (36, 24), and (0, 24). Inside the rectangle, she draws a diagonal line from (0, 0) to (36, 24). She then shades the triangular region below this diagonal. What fraction of the rectangle's area is shaded? Express your answer as a decimal. Answer: 0.5 Solution: Find the area of the rectangle. Length = 36 units, Width = 24 units. Area = 36 × 24 = 864 square units.
    Full step-by-step solution

    Step 1: Find the area of the rectangle. Length = 36 units, Width = 24 units. Area = 36 × 24 = 864 square units. Step 2: The diagonal divides the rectangle into two congruent right triangles. Each triangle has base = 36 units and height = 24 units. Step 3: Area of one triangle = (1/2) × base × height = (1/2) × 36 × 24 = 18 × 24 = 432 square units. Step 4: The shaded triangle has area 432 square units. Fraction shaded = area of triangle / area of rectangle = 432 / 864. Step 5: Simplify the fraction: 432 / 864 = 1/2. Step 6: Convert 1/2 to decimal: 1/2 = 0.5. The answer is 0.5.

  2. Olivia is designing a mosaic pattern on a coordinate grid. She draws a large square with vertices at (0, 0), (15, 0), (15, 15), and (0, 15). Inside this square, she marks a smaller square with vertices at (3, 3), (12, 3), (12, 12), and (3, 12). What fraction of the area of the large square is the area of the smaller square? Express your answer as a decimal. Answer: 0.36 Solution: Find the side length of the large square. The vertices (0,0) and (15,0) give a side length of 15 - 0 = 15 units. Find the area of the large square: 15 × 15 = 225 square units.
    Full step-by-step solution

    Step 1: Find the side length of the large square. The vertices (0,0) and (15,0) give a side length of 15 - 0 = 15 units. Step 2: Find the area of the large square: 15 × 15 = 225 square units. Step 3: Find the side length of the smaller square. The vertices (3,3) and (12,3) give a side length of 12 - 3 = 9 units. Step 4: Find the area of the smaller square: 9 × 9 = 81 square units. Step 5: Find the fraction of the area: 81/225. Step 6: Simplify the fraction. Divide numerator and denominator by 9: 81 ÷ 9 = 9, 225 ÷ 9 = 25, so 9/25. Step 7: Convert 9/25 to a decimal. 9 ÷ 25 = 0.36. The answer is 0.36.

  3. Mason is building a model of a Ferris wheel for a school project. The plans indicate that the circumference of the wheel is 7/9 of the total height of the structure. Mason needs to convert this fraction to a decimal to program a motor controller. What is 7/9 written as a repeating decimal? Use a bar over the repeating digit(s). Answer: 0.7̄ Solution: Write 7/9 as a division problem: 7 divided by 9. 9 does not go into 7, so add a decimal point and a zero: 7.0 divided by 9. 9 goes into 70 seven times (9 x 7 = 63).
    Full step-by-step solution

    Step 1: Write 7/9 as a division problem: 7 divided by 9. Step 2: 9 does not go into 7, so add a decimal point and a zero: 7.0 divided by 9. Step 3: 9 goes into 70 seven times (9 x 7 = 63). Write 7 after the decimal point, subtract 63 from 70 to get 7. Step 4: Bring down another zero to make 70. 9 goes into 70 seven times again (9 x 7 = 63). Subtract to get 7. Step 5: This pattern repeats forever. So 7/9 = 0.7777... = 0.7 with a bar over the 7. The answer is 0.7̄.

  4. Mason is helping his uncle build a custom bookshelf. The plans specify that each shelf support must be cut to a length of 2/7 of a meter. Mason's tape measure only shows decimal markings, so he needs to convert this fraction to a decimal to make an accurate cut. What is the decimal equivalent of 2/7? Express your answer as a repeating decimal using a bar over the repeating part. Answer: 0.285714̄ Solution: To convert 2/7 to a decimal, divide 2 by 7. 7 does not go into 2, so write 0 and a decimal point. Add a zero to 2 to make 20.
    Full step-by-step solution

    Step 1: To convert 2/7 to a decimal, divide 2 by 7. Step 2: 7 does not go into 2, so write 0 and a decimal point. Add a zero to 2 to make 20. Step 3: 7 goes into 20 two times (2 × 7 = 14), remainder 6. Write 2 after the decimal. Step 4: Bring down a zero to make 60. 7 goes into 60 eight times (8 × 7 = 56), remainder 4. Write 8. Step 5: Bring down a zero to make 40. 7 goes into 40 five times (5 × 7 = 35), remainder 5. Write 5. Step 6: Bring down a zero to make 50. 7 goes into 50 seven times (7 × 7 = 49), remainder 1. Write 7. Step 7: Bring down a zero to make 10. 7 goes into 10 one time (1 × 7 = 7), remainder 3. Write 1. Step 8: Bring down a zero to make 30. 7 goes into 30 four times (4 × 7 = 28), remainder 2. Write 4. Step 9: Now the remainder is 2, which is the same as the original numerator. The digits 285714 will repeat from here. So 2/7 = 0.285714285714... = 0.285714̄. The answer is 0.285714̄.

  5. 0.375 × 2.4 ÷ 0.5 = ? Answer: 1.8 Solution: Convert 0.375 to a fraction.
    Full step-by-step solution

    Step 1: Convert 0.375 to a fraction. 0.375 = 375/1000 = 3/8 Step 2: Rewrite the problem: (3/8) × 2.4 ÷ 0.5 Step 3: Convert 2.4 to a fraction: 2.4 = 24/10 = 12/5 Step 4: Convert 0.5 to a fraction: 0.5 = 1/2 Step 5: Rewrite the problem: (3/8) × (12/5) ÷ (1/2) Step 6: Division by a fraction is the same as multiplication by its reciprocal: (3/8) × (12/5) × (2/1) Step 7: Multiply the numerators: 3 × 12 × 2 = 72 Step 8: Multiply the denominators: 8 × 5 × 1 = 40 Step 9: Simplify the fraction: 72/40 = 9/5 = 1.8 Step 10: The answer is 1.8

  6. Mason is helping his grandmother create a custom birdseed mixture. The recipe calls for 5/11 of the total mixture to be sunflower seeds. Mason needs to make 16.5 kilograms of birdseed. How many kilograms of sunflower seeds does he need? Express your answer as a decimal. Answer: 7.5 Solution: We need to find 5/11 of 16.5 kilograms.
    Full step-by-step solution

    Step 1: We need to find 5/11 of 16.5 kilograms. Step 2: Multiply the fraction by the total: (5/11) * 16.5 Step 3: Rewrite 16.5 as a fraction: 16.5 = 33/2 Step 4: Multiply: (5/11) * (33/2) = (5 * 33) / (11 * 2) = 165 / 22 Step 5: Simplify: 165 ÷ 22 = 7.5 Step 6: The answer is 7.5 kilograms. The answer is 7.5.

  7. Emma is conducting a science experiment to create a special plant fertilizer solution. She needs to mix 2.25 liters of concentrated nutrient liquid with water to make a total of 15 liters of usable fertilizer. What fraction of the final solution is the concentrated nutrient liquid? Express your answer as a simplified fraction. Answer: 3/20 Solution: Identify the part (concentrated nutrient) and the whole (total solution) Part = 2.25 liters Whole = 15 liters Write the fraction representing the part over the whole Fraction = 2.25 / 15 Convert 2.25 to a fraction 2.25 = 225/100 = 9/4 (9/4) ÷ 15 = (9/4) × (1/15) = 9/60 9/60 = 3/20 The answer is…
    Full step-by-step solution

    Step 1: Identify the part (concentrated nutrient) and the whole (total solution) Part = 2.25 liters Whole = 15 liters Step 2: Write the fraction representing the part over the whole Fraction = 2.25 / 15 Step 3: Convert 2.25 to a fraction 2.25 = 225/100 = 9/4 Step 4: Divide the fractions (9/4) ÷ 15 = (9/4) × (1/15) = 9/60 Step 5: Simplify the fraction 9/60 = 3/20 The answer is 3/20.