Decimal Notation

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Answer Key & Explanations

Decimal Notation · Grade 4 · Worksheet 3

1. Aroha is helping her grandmother measure ingredients for a large family dinner. She needs 2.65 kilograms of potatoes for the roast and 1.35 kilograms of potatoes for the mash. What is the total weight of potatoes Aroha needs in decimal form? Answer: 4.00 Solution: Write the two amounts with the decimal points lined up: 2.65 + 1.35 Add the hundredths place: 5 + 5 = 10. Write 0 in the hundredths place and carry 1 to the tenths place. Add the tenths place: 6 + 3 + 1 (carried) = 10.
   Full step-by-step solution

   Step 1: Write the two amounts with the decimal points lined up: 2.65 + 1.35 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: 6 + 3 + 1 (carried) = 10. Write 0 in the tenths place and carry 1 to the ones place. Step 4: Add the ones place: 2 + 1 + 1 (carried) = 4. Write 4 in the ones place. Step 5: Combine all places: 4.00 The total weight of potatoes Aroha needs is 4.00 kilograms.

2. A rectangular swimming pool is drawn with a length of 15.75 meters and a width of 8.5 meters. What is the area of the pool in square meters? Answer: 133.875 Solution: Identify the formula for the area of a rectangle: Area = length × width. Write down the given measurements: length = 15.75 m, width = 8.5 m. Multiply the numbers: 15.75 × 8.5.
   Full step-by-step solution

   Step 1: Identify the formula for the area of a rectangle: Area = length × width. Step 2: Write down the given measurements: length = 15.75 m, width = 8.5 m. Step 3: Multiply the numbers: 15.75 × 8.5. Step 4: First, multiply 15.75 by 8: 15.75 × 8 = 126. Step 5: Then, multiply 15.75 by 0.5: 15.75 × 0.5 = 7.875. Step 6: Add the two results: 126 + 7.875 = 133.875. Step 7: The area of the pool is 133.875 square meters.

3. Liam is building a rectangular garden in his backyard. The garden measures 3.5 meters in length and 2.25 meters in width. What is the total area of Liam's garden in square meters? Answer: 7.875 Solution: To find the area of a rectangle, we multiply its length by its width. Write down the given measurements. Length = 3.5 meters Width = 2.25 meters Write the area formula.
   Full step-by-step solution

   To find the area of a rectangle, we multiply its length by its width. Step 1: Write down the given measurements. Length = 3.5 meters Width = 2.25 meters Step 2: Write the area formula. Area = Length × Width Step 3: Substitute the values into the formula. Area = 3.5 × 2.25 Step 4: To make the multiplication easier, we can convert the decimals into fractions. 3.5 is the same as 35/10. 2.25 is the same as 225/100. Step 5: Multiply the two fractions. Area = (35/10) × (225/100) Step 6: Multiply the numerators together and the denominators together. Numerator: 35 × 225 Denominator: 10 × 100 Step 7: Calculate the numerator. First, calculate 35 × 200 = 7000. Then, calculate 35 × 25 = 875. Now, add them together: 7000 + 875 = 7875. So, the numerator is 7875. Step 8: Calculate the denominator. 10 × 100 = 1000. So, the denominator is 1000. Step 9: Write the result as a fraction. Area = 7875 / 1000 Step 10: Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 125. 7875 ÷ 125 = 63 1000 ÷ 125 = 8 So, the simplified fraction is 63/8. Step 11: Convert the fraction 63/8 back to a decimal by performing the division. 63 ÷ 8 = 7.875 Therefore, the total area of Liam's garden is 7.875 square meters.

4. 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.

5. Sophia sees a number line diagram that starts at 0 and ends at 1. The space between 0 and 1 is divided into 10 equal parts, and the space between each of those parts is further divided into 10 smaller equal parts. A point is marked at 7 of the large tenths marks and 4 of the small hundredths marks past the 0. What decimal number does the point represent? Answer: 0.74 Solution: Step 2: Each tenth is divided into 10 smaller parts, so each small part represents 0.01 (one hundredth). Step 3: The point is at 7 tenths and 4 hundredths. Step 4: 7 tenths = 0.7, and 4 hundredths = 0.04.
   Full step-by-step solution

   Step 1: The number line from 0 to 1 is divided into 10 equal parts, each representing 0.1 (one tenth). Step 2: Each tenth is divided into 10 smaller parts, so each small part represents 0.01 (one hundredth). Step 3: The point is at 7 tenths and 4 hundredths. Step 4: 7 tenths = 0.7, and 4 hundredths = 0.04. Step 5: Add them together: 0.7 + 0.04 = 0.74. The point represents the decimal 0.74.