Worksheet 1Worksheet 2Worksheet 3

The download includes this worksheet followed by the answer key with explanations. In the print dialog choose “Save as PDF” to download.

lessonbunny.com
Name: ______________________________ Date: ______________

Rational to Decimal

Grade 7 · Decimals · Worksheet 2

  1. 0.6 × (1.25 + 0.75) ÷ 0.4 = ? 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. Convert 11/15 to decimal. Answer: ______________
  4. A factory produces 12500 units of a product every day. The quality control department finds that 0.048 of these units are defective. How many defective units are produced daily? Express your answer as a decimal number. Answer: ______________
  5. Convert 7/12 to decimal. Answer: ______________
  6. Mason is building a wooden model of a bridge for his engineering class. The plans call for a support beam that is 11/16 of a meter long. He needs to cut this from a piece of wood that is measured in decimal meters on the ruler. What is the exact decimal equivalent of 11/16 of a meter? Answer: ______________
  7. Olivia is baking a special bread for her family. The recipe calls for 3/7 of a cup of honey, but she only has a measuring cup marked in decimals. She needs to convert this fraction to a decimal to measure the honey accurately. What is 3/7 written as a repeating decimal? Use a bar notation to indicate the repeating part. Answer: ______________
  8. Mason draws a large square on a coordinate plane with vertices at (0, 0), (12, 0), (12, 12), and (0, 12). Inside the square, he shades a smaller square with vertices at (2, 2), (7, 2), (7, 7), and (2, 7). What fraction of the large square is shaded? Express your answer as a decimal. Answer: ______________
lessonbunny.com

Answer Key & Explanations

Rational to Decimal · Grade 7 · Worksheet 2

  1. 0.6 × (1.25 + 0.75) ÷ 0.4 = ? Answer: 3 Solution: First, solve the expression inside the parentheses: 1.25 + 0.75 = 2.00 Now the expression becomes: 0.6 × 2.00 ÷ 0.4 Perform multiplication and division from left to right: 0.6 × 2.00 = 1.20 Now divide: 1.20 ÷ 0.4 = 3.00 The final answer is 3.
    Full step-by-step solution

    Step 1: First, solve the expression inside the parentheses: 1.25 + 0.75 = 2.00 Step 2: Now the expression becomes: 0.6 × 2.00 ÷ 0.4 Step 3: Perform multiplication and division from left to right: 0.6 × 2.00 = 1.20 Step 4: Now divide: 1.20 ÷ 0.4 = 3.00 Step 5: The final answer is 3.

  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. Convert 11/15 to decimal. Answer: 0.73̄ Solution: Divide 11 by 15. 15 goes into 11 zero times, so add a decimal point and a zero: 110. 15 goes into 110 seven times (15 × 7 = 105), remainder 5.
    Full step-by-step solution

    Step 1: Divide 11 by 15. 15 goes into 11 zero times, so add a decimal point and a zero: 110. Step 2: 15 goes into 110 seven times (15 × 7 = 105), remainder 5. Step 3: Bring down a zero: 50. 15 goes into 50 three times (15 × 3 = 45), remainder 5. Step 4: Notice the remainder 5 repeats. Each time we bring down a zero, we get 50, and 15 goes into 50 three times with remainder 5. So the digit '3' will repeat forever. Step 5: The decimal is 0.73333... which is written as 0.73̄ (the bar over the 3 shows it repeats). The answer is 0.73̄.

  4. A factory produces 12500 units of a product every day. The quality control department finds that 0.048 of these units are defective. How many defective units are produced daily? Express your answer as a decimal number. Answer: 600.0 Solution: We know the factory produces 12500 units per day. The fraction of defective units is 0.048. We need to find the number of defective units.
    Full step-by-step solution

    Step 1: Understand the problem. We know the factory produces 12500 units per day. The fraction of defective units is 0.048. We need to find the number of defective units. Step 2: Interpret 0.048. 0.048 means 0.048 out of 1, or 4.8% of the total units. Step 3: Set up the calculation. Number of defective units = Total units × Fraction defective = 12500 × 0.048 Step 4: Multiply step-by-step. First, multiply 12500 by 0.04: 12500 × 0.04 = 12500 × 4 / 100 12500 × 4 = 50000 50000 / 100 = 500 Second, multiply 12500 by 0.008: 12500 × 0.008 = 12500 × 8 / 1000 12500 × 8 = 100000 100000 / 1000 = 100 Step 5: Add the two results. 500 + 100 = 600 Step 6: Express as a decimal number. The problem asks for the answer as a decimal number, so 600.0 is correct. Final answer: 600.0

  5. Convert 7/12 to decimal. Answer: 0.583̄ Solution: Divide 7 by 12. 12 goes into 7 zero times, so we add a decimal point and a zero: 70. 12 goes into 70 five times (12 × 5 = 60), remainder 10.
    Full step-by-step solution

    Step 1: Divide 7 by 12. 12 goes into 7 zero times, so we add a decimal point and a zero: 70. Step 2: 12 goes into 70 five times (12 × 5 = 60), remainder 10. Step 3: Bring down a zero: 100. 12 goes into 100 eight times (12 × 8 = 96), remainder 4. Step 4: Bring down a zero: 40. 12 goes into 40 three times (12 × 3 = 36), remainder 4. Step 5: Notice the remainder 4 repeats. Each time we bring down a zero, we get 40, and 12 goes into 40 three times with remainder 4. So the digits '3' will repeat forever. Step 6: The decimal is 0.58333... which is written as 0.583̄ (the bar over the 3 shows it repeats). The answer is 0.583̄.

  6. Mason is building a wooden model of a bridge for his engineering class. The plans call for a support beam that is 11/16 of a meter long. He needs to cut this from a piece of wood that is measured in decimal meters on the ruler. What is the exact decimal equivalent of 11/16 of a meter? Answer: 0.6875 Solution: To convert the fraction 11/16 to a decimal, divide the numerator (11) by the denominator (16). Perform the division: 11 ÷ 16 = 0.6875. Since 16 × 0.6875 = 11 exactly, this is a terminating decimal.
    Full step-by-step solution

    Step 1: To convert the fraction 11/16 to a decimal, divide the numerator (11) by the denominator (16). Step 2: Perform the division: 11 ÷ 16 = 0.6875. Step 3: Since 16 × 0.6875 = 11 exactly, this is a terminating decimal. The exact decimal equivalent of 11/16 of a meter is 0.6875 meters.

  7. Olivia is baking a special bread for her family. The recipe calls for 3/7 of a cup of honey, but she only has a measuring cup marked in decimals. She needs to convert this fraction to a decimal to measure the honey accurately. What is 3/7 written as a repeating decimal? Use a bar notation to indicate the repeating part. Answer: 0.428571̄ Solution: Write the fraction as a division problem: 3 divided by 7. Perform long division: 7 goes into 3 zero times, so add a decimal point and a zero: 30. 7 goes into 30 four times (28), remainder 2.
    Full step-by-step solution

    Step 1: Write the fraction as a division problem: 3 divided by 7. Step 2: Perform long division: 7 goes into 3 zero times, so add a decimal point and a zero: 30. 7 goes into 30 four times (28), remainder 2. Step 3: Bring down a zero: 20. 7 goes into 20 two times (14), remainder 6. Step 4: Bring down a zero: 60. 7 goes into 60 eight times (56), remainder 4. Step 5: Bring down a zero: 40. 7 goes into 40 five times (35), remainder 5. Step 6: Bring down a zero: 50. 7 goes into 50 seven times (49), remainder 1. Step 7: Bring down a zero: 10. 7 goes into 10 one time (7), remainder 3. Step 8: Notice the remainder is 3, which is where we started. The digits 428571 will repeat. Step 9: Therefore, 3/7 = 0.428571428571... = 0.428571̄. The answer is 0.428571̄.

  8. Mason draws a large square on a coordinate plane with vertices at (0, 0), (12, 0), (12, 12), and (0, 12). Inside the square, he shades a smaller square with vertices at (2, 2), (7, 2), (7, 7), and (2, 7). What fraction of the large square is shaded? Express your answer as a decimal. Answer: 0.173611... (or 25/144) Solution: Find the area of the large square. The side length is from x=0 to x=12, so side = 12 units. Area = side × side = 12 × 12 = 144 square units.
    Full step-by-step solution

    Step 1: Find the area of the large square. The side length is from x=0 to x=12, so side = 12 units. Area = side × side = 12 × 12 = 144 square units. Step 2: Find the area of the shaded square. The side length is from x=2 to x=7, so side = 7 - 2 = 5 units. Area = 5 × 5 = 25 square units. Step 3: Write the shaded area as a fraction of the total area: 25/144. Step 4: Convert the fraction to a decimal by dividing 25 by 144. 144 goes into 25 zero times, so we add a decimal and zeros. 144 goes into 250 once (144), remainder 106. Bring down a zero: 1060. 144 goes into 1060 seven times (1008), remainder 52. Bring down a zero: 520. 144 goes into 520 three times (432), remainder 88. Bring down a zero: 880. 144 goes into 880 six times (864), remainder 16. Bring down a zero: 160. 144 goes into 160 once (144), remainder 16. Notice the remainder 16 repeats from the step with 160, so the digits 173611 will repeat. The decimal is 0.173611... with the digits 173611 repeating. The answer is 0.173611... (or 25/144).