Decimal Notation

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Answer Key & Explanations

Decimal Notation · Grade 4 · Worksheet 2

1. What is the value of 7 in 5.78? Answer: 0.7 Solution: Identify the position of the digit 7 in the number 5.78 The digit 7 is in the tenths place (first digit after the decimal point) A digit in the tenths place represents that number divided by 10 7 in the tenths place means 7/10 = 0.7 Therefore, the value of 7 in 5.78 is 0.7 The answer is 0.7.
   Full step-by-step solution

   Step 1: Identify the position of the digit 7 in the number 5.78 Step 2: The digit 7 is in the tenths place (first digit after the decimal point) Step 3: A digit in the tenths place represents that number divided by 10 Step 4: 7 in the tenths place means 7/10 = 0.7 Step 5: Therefore, the value of 7 in 5.78 is 0.7 The answer is 0.7.

2. Emma is baking cookies for a school bake sale. She needs 0.75 cups of sugar for one batch of chocolate chip cookies and 0.5 cups of sugar for one batch of oatmeal raisin cookies. If she wants to make 3 batches of chocolate chip cookies and 2 batches of oatmeal raisin cookies, how many total cups of sugar will Emma need? Answer: 3.25 Solution: Emma needs 0.75 cups per batch and makes 3 batches 0.75 × 3 = 2.25 cups Emma needs 0.5 cups per batch and makes 2 batches 0.5 × 2 = 1.0 cups 2.25 + 1.0 = 3.25 cups Emma will need 3.25 total cups of sugar.
   Full step-by-step solution

   Step 1: Calculate sugar needed for chocolate chip cookies Emma needs 0.75 cups per batch and makes 3 batches 0.75 × 3 = 2.25 cups Step 2: Calculate sugar needed for oatmeal raisin cookies Emma needs 0.5 cups per batch and makes 2 batches 0.5 × 2 = 1.0 cups Step 3: Add both amounts together 2.25 + 1.0 = 3.25 cups Emma will need 3.25 total cups of sugar.

3. A rectangular swimming pool is drawn with a length of 15.25 meters and a width of 8.5 meters. What is the area of the pool in square meters? Answer: 129.625 Solution: The area of a rectangle is found by multiplying its length by its width. Multiply 15.25 by 8.5.
   Full step-by-step solution

   Step 1: The area of a rectangle is found by multiplying its length by its width. Step 2: Multiply 15.25 by 8.5. Step 3: First, multiply 15.25 by 8: 15.25 × 8 = 122 Step 4: Next, multiply 15.25 by 0.5: 15.25 × 0.5 = 7.625 Step 5: Add the two results: 122 + 7.625 = 129.625 Step 6: The area is 129.625 square meters.

4. A rectangular playground is drawn with a length of 12.5 meters and a width of 8.4 meters. What is the perimeter of the playground in meters? Answer: 41.8 Solution: The formula for perimeter of a rectangle is P = 2 × (length + width) Substitute the given values: P = 2 × (12.5 + 8.4) Add inside the parentheses: 12.5 + 8.4 = 20.9 Multiply by 2: 2 × 20.9 = 41.8 The perimeter is 41.8 meters.
   Full step-by-step solution

   Step 1: The formula for perimeter of a rectangle is P = 2 × (length + width) Step 2: Substitute the given values: P = 2 × (12.5 + 8.4) Step 3: Add inside the parentheses: 12.5 + 8.4 = 20.9 Step 4: Multiply by 2: 2 × 20.9 = 41.8 Step 5: The perimeter is 41.8 meters.

5. 3.75 + 2.45 = ? Answer: 6.20 Solution: 3.75 + 2.45 Add the hundredths place: 5 + 5 = 10. Write 0 in the hundredths place and carry 1 to the tenths place. Add the tenths place: 7 + 4 + 1 (carried) = 12.
   Full step-by-step solution

   Step 1: Write the numbers with decimal points aligned: 3.75 + 2.45 Step 2: Add the hundredths place: 5 + 5 = 10. Write 0 in the hundredths place and carry 1 to the tenths place. Step 3: Add the tenths place: 7 + 4 + 1 (carried) = 12. Write 2 in the tenths place and carry 1 to the ones place. Step 4: Add the ones place: 3 + 2 + 1 (carried) = 6. Write 6 in the ones place. Step 5: Place the decimal point in the answer directly below the decimal points in the numbers being added. The final answer is 6.20.

6. 4.25 × 3.6 = ? Answer: 15.3 Solution: Multiply 4.25 × 3.6 as if they were whole numbers: 425 × 36 425 × 30 = 12,750 425 × 6 = 2,550 Add the results: 12,750 + 2,550 = 15,300 Count the decimal places: 4.25 has 2 decimal places, 3.6 has 1 decimal place, so total decimal places = 3 Place the decimal point in 15,300 to get 3 decimal…
   Full step-by-step solution

   Step 1: Multiply 4.25 × 3.6 as if they were whole numbers: 425 × 36 Step 2: 425 × 30 = 12,750 Step 3: 425 × 6 = 2,550 Step 4: Add the results: 12,750 + 2,550 = 15,300 Step 5: Count the decimal places: 4.25 has 2 decimal places, 3.6 has 1 decimal place, so total decimal places = 3 Step 6: Place the decimal point in 15,300 to get 3 decimal places: 15.300 = 15.3 The answer is 15.3.