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Decimal-Fraction Equivalence

Grade 4 · Fractions · Worksheet 1

  1. A rectangular garden is divided into 100 equal squares. If 48 squares are planted with tomatoes and 27 squares are planted with peppers, what decimal represents the portion of the garden that has vegetables planted? Answer: ______________
  2. Noah is building a wooden frame for a school project. He needs a piece of wood that is 0.25 meters long, but his ruler only shows centimeters. How many centimeters long does the piece of wood need to be? Answer: ______________
  3. A rectangular field is divided into a 10 by 10 grid of equal squares. The farmer plants corn in 47 of these squares. What decimal represents the portion of the field planted with corn? Answer: ______________
  4. A rectangular garden is divided into 10 equal sections along its length. If 3 sections are planted with carrots, what decimal represents the fraction of the garden that has carrots? Answer: ______________
  5. Liam is measuring ribbon for a craft project. He needs 0.75 meters of blue ribbon and 3/4 meter of red ribbon. Are these two lengths equal?
    • A. yes
    • B. no
  6. A rectangular garden is divided into 100 equal squares. If 35 of these squares are planted with carrots, what decimal represents the portion of the garden that has carrots? Answer: ______________
  7. A rectangular field is divided into 100 equal squares. The farmer plants corn in 48 squares and wheat in the remaining squares. What decimal represents the portion of the field planted with wheat? Answer: ______________
  8. 0.6 = ?/10 Answer: ______________
  9. Liam is measuring ribbon for a craft project. He needs 0.75 meters of blue ribbon and 3/4 of a meter of red ribbon. Are these two lengths equivalent?
    • A. no
    • B. yes
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Answer Key & Explanations

Decimal-Fraction Equivalence · Grade 4 · Worksheet 1

  1. A rectangular garden is divided into 100 equal squares. If 48 squares are planted with tomatoes and 27 squares are planted with peppers, what decimal represents the portion of the garden that has vegetables planted? Answer: 0.75 Solution: Find the total number of squares planted with vegetables 48 squares (tomatoes) + 27 squares (peppers) = 75 squares 75 squares out of 100 total squares = 75/100 75/100 = 0.75 The answer is 0.75.
    Full step-by-step solution

    Step 1: Find the total number of squares planted with vegetables 48 squares (tomatoes) + 27 squares (peppers) = 75 squares Step 2: Convert this to a fraction of the whole garden 75 squares out of 100 total squares = 75/100 Step 3: Convert the fraction to a decimal 75/100 = 0.75 The answer is 0.75.

  2. Noah is building a wooden frame for a school project. He needs a piece of wood that is 0.25 meters long, but his ruler only shows centimeters. How many centimeters long does the piece of wood need to be? Answer: 25 Solution: We know that 1 meter is equal to 100 centimeters. Noah needs 0.25 meters of wood. To find the length in centimeters, multiply the number of meters by the number of centimeters in one meter: 0.25 * 100.
    Full step-by-step solution

    Step 1: We know that 1 meter is equal to 100 centimeters. Step 2: Noah needs 0.25 meters of wood. Step 3: To find the length in centimeters, multiply the number of meters by the number of centimeters in one meter: 0.25 * 100. Step 4: 0.25 * 100 = 25. The piece of wood needs to be 25 centimeters long.

  3. A rectangular field is divided into a 10 by 10 grid of equal squares. The farmer plants corn in 47 of these squares. What decimal represents the portion of the field planted with corn? Answer: 0.47 Solution: Find the total number of squares in the grid. Since it's a 10 by 10 grid, there are 10 × 10 = 100 total squares. Determine the fraction of squares planted with corn.
    Full step-by-step solution

    Step 1: Find the total number of squares in the grid. Since it's a 10 by 10 grid, there are 10 × 10 = 100 total squares. Step 2: Determine the fraction of squares planted with corn. This is 47 out of 100, or 47/100. Step 3: Convert the fraction to a decimal. Since the denominator is 100, the decimal is 0.47. The answer is 0.47.

  4. A rectangular garden is divided into 10 equal sections along its length. If 3 sections are planted with carrots, what decimal represents the fraction of the garden that has carrots? Answer: 0.3 Solution: The garden is divided into 10 equal sections. 3 sections are planted with carrots. Write the fraction of the garden with carrots.
    Full step-by-step solution

    Step 1: Understand the problem. The garden is divided into 10 equal sections. 3 sections are planted with carrots. Step 2: Write the fraction of the garden with carrots. That is 3 sections out of 10 total sections, so the fraction is 3/10. Step 3: Convert the fraction to a decimal. The fraction 3/10 means 3 divided by 10. Step 4: Perform the division. 3 divided by 10 is 0.3. Step 5: Conclusion. The decimal that represents the fraction of the garden with carrots is 0.3.

  5. Liam is measuring ribbon for a craft project. He needs 0.75 meters of blue ribbon and 3/4 meter of red ribbon. Are these two lengths equal? Answer: A. yes Solution: We need to compare 0.75 meters of blue ribbon and 3/4 meter of red ribbon to see if they are equal. Write both lengths in the same form. 0.75 is a decimal.
    Full step-by-step solution

    Step 1: Understand the problem. We need to compare 0.75 meters of blue ribbon and 3/4 meter of red ribbon to see if they are equal. Step 2: Write both lengths in the same form. 0.75 is a decimal. 3/4 is a fraction. Step 3: Convert the fraction 3/4 to a decimal. To convert 3/4 to a decimal, divide 3 by 4. 3 ÷ 4 = 0.75. Step 4: Compare the two lengths. Blue ribbon: 0.75 meters Red ribbon: 3/4 meters = 0.75 meters Step 5: Conclusion. Since 0.75 = 0.75, the two lengths are equal. Answer: yes

  6. A rectangular garden is divided into 100 equal squares. If 35 of these squares are planted with carrots, what decimal represents the portion of the garden that has carrots? Answer: 0.35 Solution: The garden is divided into 100 equal squares. 35 of these squares are planted with carrots. Determine the fraction of the garden with carrots.
    Full step-by-step solution

    Step 1: Understand the problem. The garden is divided into 100 equal squares. 35 of these squares are planted with carrots. Step 2: Determine the fraction of the garden with carrots. The fraction is the number of carrot squares divided by the total number of squares. So, fraction = 35 / 100. Step 3: Convert the fraction to a decimal. 35 divided by 100 means moving the decimal point in 35 two places to the left. 35 is the same as 35.0, so moving the decimal two places left gives 0.35. Step 4: Conclusion. The portion of the garden with carrots is 0.35.

  7. A rectangular field is divided into 100 equal squares. The farmer plants corn in 48 squares and wheat in the remaining squares. What decimal represents the portion of the field planted with wheat? Answer: 0.52 Solution: Find the total number of squares: 100 Find the number of squares planted with wheat: 100 - 48 = 52 Write the fraction of wheat squares: 52/100 Convert the fraction to a decimal: 52/100 = 0.52 The decimal representing the portion planted with wheat is 0.52
    Full step-by-step solution

    Step 1: Find the total number of squares: 100 Step 2: Find the number of squares planted with wheat: 100 - 48 = 52 Step 3: Write the fraction of wheat squares: 52/100 Step 4: Convert the fraction to a decimal: 52/100 = 0.52 Step 5: The decimal representing the portion planted with wheat is 0.52

  8. 0.6 = ?/10 Answer: 6 Solution: The decimal 0.6 means 6 tenths In fraction form, tenths are written with denominator 10 So 0.6 = 6/10 The numerator is 6 The answer is 6.
    Full step-by-step solution

    Step 1: The decimal 0.6 means 6 tenths Step 2: In fraction form, tenths are written with denominator 10 Step 3: So 0.6 = 6/10 Step 4: The numerator is 6 The answer is 6.

  9. Liam is measuring ribbon for a craft project. He needs 0.75 meters of blue ribbon and 3/4 of a meter of red ribbon. Are these two lengths equivalent? Answer: B. yes Solution: We need to compare 0.75 meters of blue ribbon and 3/4 of a meter of red ribbon to see if they are equal. Write the two lengths as numbers.
    Full step-by-step solution

    Step 1: Understand the problem. We need to compare 0.75 meters of blue ribbon and 3/4 of a meter of red ribbon to see if they are equal. Step 2: Write the two lengths as numbers. Blue ribbon: 0.75 meters Red ribbon: 3/4 meters Step 3: Convert the fraction 3/4 into a decimal to compare easily. To convert 3/4 to a decimal, divide 3 by 4. 3 ÷ 4 = 0.75 Step 4: Compare the two lengths. Blue ribbon = 0.75 meters Red ribbon = 0.75 meters Step 5: Conclusion. Since both lengths are 0.75 meters, they are equivalent. Answer: yes