Decimal Notation

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Answer Key & Explanations

Decimal Notation · Grade 4 · Worksheet 1

1. Liam is measuring the weight of fruits for a smoothie recipe. He uses 1.35 kilograms of bananas and 2.47 kilograms of strawberries. What is the total weight of fruit Liam uses for his smoothie in kilograms? Answer: 3.82 Solution: Write the numbers with decimal points lined up: 1.35 + 2.47 Add the hundredths place: 5 hundredths + 7 hundredths = 12 hundredths. Write 2 in the hundredths place and carry 1 to the tenths place.
   Full step-by-step solution

   Step 1: Write the numbers with decimal points lined up: 1.35 + 2.47 Step 2: Add the hundredths place: 5 hundredths + 7 hundredths = 12 hundredths. Write 2 in the hundredths place and carry 1 to the tenths place. Step 3: Add the tenths place: 3 tenths + 4 tenths + 1 carried tenth = 8 tenths. Write 8 in the tenths place. Step 4: Add the ones place: 1 one + 2 ones = 3 ones. Write 3 in the ones place. Step 5: Bring down the decimal point. Final result: 3.82 Liam uses 3.82 kilograms of fruit for his smoothie.

2. Emma is baking cookies for a school bake sale. She needs 2.75 cups of flour for the chocolate chip cookies and 1.5 cups of flour for the oatmeal raisin cookies. How many cups of flour does Emma need in total? Answer: 4.25 Solution: Identify the amounts of flour needed: 2.75 cups for chocolate chip cookies and 1.5 cups for oatmeal raisin cookies.
   Full step-by-step solution

   Step 1: Identify the amounts of flour needed: 2.75 cups for chocolate chip cookies and 1.5 cups for oatmeal raisin cookies. Step 2: Set up the addition problem: 2.75 + 1.5 Step 3: Align the decimal points and add: 2.75 + 1.50 = 4.25 Step 4: Emma needs 4.25 cups of flour in total.

3. Isabella is helping her grandmother measure ingredients for a special family recipe. The recipe calls for 2.7 cups of flour and 1.2 cups of sugar. Isabella writes the total amount of flour and sugar as a decimal number. What is the total amount, written as a decimal? Answer: 3.9 Solution: Write the amounts: 2.7 cups of flour and 1.2 cups of sugar. Add the whole number parts: 2 + 1 = 3. Add the tenths parts: 0.7 + 0.2 = 0.9.
   Full step-by-step solution

   Step 1: Write the amounts: 2.7 cups of flour and 1.2 cups of sugar. Step 2: Add the whole number parts: 2 + 1 = 3. Step 3: Add the tenths parts: 0.7 + 0.2 = 0.9. Step 4: Combine the whole number and tenths: 3 + 0.9 = 3.9. The total amount is 3.9 cups.

4. 4.75 + 3.25 = ? Answer: 8.00 Solution: Write the numbers with decimal points aligned: 4.75 + 3.25 Add the hundredths place: 5 + 5 = 10. Write 0 in the hundredths place and carry over 1 to the tenths place. Add the tenths place: 7 + 2 + 1 (carried over) = 10.
   Full step-by-step solution

   Step 1: Write the numbers with decimal points aligned: 4.75 + 3.25 Step 2: Add the hundredths place: 5 + 5 = 10. Write 0 in the hundredths place and carry over 1 to the tenths place. Step 3: Add the tenths place: 7 + 2 + 1 (carried over) = 10. Write 0 in the tenths place and carry over 1 to the ones place. Step 4: Add the ones place: 4 + 3 + 1 (carried over) = 8. Write 8 in the ones place. Step 5: Place the decimal point in the answer: 8.00 The answer is 8.00.

5. 3.75 + 2.25 = ? Answer: 6.00 Solution: Write the numbers one under the other, aligning the decimal points. 3.75 + 2.25 Start adding from the rightmost column (hundredths place). 5 hundredths + 5 hundredths = 10 hundredths.
   Full step-by-step solution

   Let's add 3.75 and 2.25 step by step. Step 1: Write the numbers one under the other, aligning the decimal points. 3.75 + 2.25 ________ Step 2: Start adding from the rightmost column (hundredths place). 5 hundredths + 5 hundredths = 10 hundredths. Since 10 hundredths equals 1 tenth and 0 hundredths, write 0 in the hundredths place and carry over 1 to the tenths place. Step 3: Add the tenths place, including the carry-over. 7 tenths + 2 tenths + 1 tenth (carry-over) = 10 tenths. Since 10 tenths equals 1 whole and 0 tenths, write 0 in the tenths place and carry over 1 to the units place. Step 4: Add the units place, including the carry-over. 3 units + 2 units + 1 unit (carry-over) = 6 units. Write 6 in the units place. Step 5: Place the decimal point in the answer directly below the decimal points in the problem. The result is 6.00. So, 3.75 + 2.25 = 6.00.

6. Liam is building a rectangular garden in his backyard. The garden measures 4.5 meters long and 3.2 meters wide. What is the total area of Liam's garden in square meters? Answer: 14.4 Solution: To find the area of a rectangle, we multiply the length by the width. Write down the given measurements. Length = 4.5 meters Width = 3.2 meters Write the formula for the area of a rectangle.
   Full step-by-step solution

   To find the area of a rectangle, we multiply the length by the width. Step 1: Write down the given measurements. Length = 4.5 meters Width = 3.2 meters Step 2: Write the formula for the area of a rectangle. Area = Length × Width Step 3: Substitute the given numbers into the formula. Area = 4.5 × 3.2 Step 4: Perform the multiplication. First, multiply the numbers as if they were whole numbers. 45 × 32 = 1440 Step 5: Determine where to place the decimal point. The original numbers, 4.5 and 3.2, have one digit after the decimal point each. This is a total of two decimal places. Therefore, the product must also have two digits after the decimal point. Step 6: Place the decimal point in the product. 1440 becomes 14.40 Step 7: Simplify the result. 14.40 is the same as 14.4 Final Answer: The total area of Liam's garden is 14.4 square meters.

7. What is the value of the digit 6 in 7.36? Answer: 0.06 Solution: Identify the position of the digit 6 in the number 7.36. The digit 6 is in the second position after the decimal point. The first position after the decimal is tenths, and the second position is hundredths.
   Full step-by-step solution

   Step 1: Identify the position of the digit 6 in the number 7.36. Step 2: The digit 6 is in the second position after the decimal point. Step 3: The first position after the decimal is tenths, and the second position is hundredths. Step 4: A digit in the hundredths place represents that number divided by 100. Step 5: Therefore, 6 in the hundredths place means 6/100 = 0.06. The answer is 0.06.