Decimal Notation

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Answer Key & Explanations

Decimal Notation · Grade 4 · Worksheet 1

1. Emma is baking cookies for her class party. She needs 0.75 cups of sugar for the chocolate chip cookies and 0.5 cups of sugar for the oatmeal cookies. How many cups of sugar does Emma need in total? Answer: 1.25 Solution: Identify the amounts needed: 0.75 cups for chocolate chip cookies and 0.5 cups for oatmeal cookies Add the two amounts together: 0.75 + 0.5 Line up the decimal points and add: 0.75 + 0.50 = 1.25 Emma needs 1.25 cups of sugar in total.
   Full step-by-step solution

   Step 1: Identify the amounts needed: 0.75 cups for chocolate chip cookies and 0.5 cups for oatmeal cookies Step 2: Add the two amounts together: 0.75 + 0.5 Step 3: Line up the decimal points and add: 0.75 + 0.50 = 1.25 Step 4: Emma needs 1.25 cups of sugar in total.

2. Isabella is helping her mom measure ingredients for a special pancake recipe. The recipe calls for 2.35 cups of buttermilk. Isabella pours 1.20 cups of buttermilk into the bowl. How many more cups of buttermilk does she need to add to reach the correct amount? Answer: 1.15 Solution: Write the total needed and the amount already added: 2.35 cups needed, 1.20 cups added. Subtract the hundredths: 5 hundredths minus 0 hundredths = 5 hundredths. Subtract the tenths: 3 tenths minus 2 tenths = 1 tenth.
   Full step-by-step solution

   Step 1: Write the total needed and the amount already added: 2.35 cups needed, 1.20 cups added. Step 2: Subtract the hundredths: 5 hundredths minus 0 hundredths = 5 hundredths. Step 3: Subtract the tenths: 3 tenths minus 2 tenths = 1 tenth. Step 4: Subtract the ones: 2 ones minus 1 one = 1 one. Step 5: Combine the places: 1 one, 1 tenth, 5 hundredths = 1.15. Isabella needs to add 1.15 cups of buttermilk.

3. What is the value of the digit 7 in 9.37? Answer: 0.07 Solution: Identify the position of the digit 7 in the number 9.37 The digit 7 is in the second position after the decimal point The first position after the decimal is tenths, the second position is hundredths A digit in the hundredths place represents that number divided by 100 Therefore, 7 in the…
   Full step-by-step solution

   Step 1: Identify the position of the digit 7 in the number 9.37 Step 2: The digit 7 is in the second position after the decimal point Step 3: The first position after the decimal is tenths, the second position is hundredths Step 4: A digit in the hundredths place represents that number divided by 100 Step 5: Therefore, 7 in the hundredths place means 7/100 = 0.07 The answer is 0.07.

4. Emma is measuring fabric for a school project. She needs 2.75 meters of blue fabric and 1.85 meters of red fabric. How many meters of fabric does Emma need in total? Answer: 4.6 Solution: Write down the two amounts: 2.75 meters and 1.85 meters Add the whole numbers: 2 + 1 = 3 Add the decimal parts: 0.75 + 0.85 = 1.60 Combine the results: 3 + 1.60 = 4.60 Simplify: 4.60 is the same as 4.6 Emma needs 4.6 meters of fabric in total.
   Full step-by-step solution

   Step 1: Write down the two amounts: 2.75 meters and 1.85 meters Step 2: Add the whole numbers: 2 + 1 = 3 Step 3: Add the decimal parts: 0.75 + 0.85 = 1.60 Step 4: Combine the results: 3 + 1.60 = 4.60 Step 5: Simplify: 4.60 is the same as 4.6 Emma needs 4.6 meters of fabric in total.

5. Hana is helping her mother measure ingredients for a large family dinner. She measures 2.65 kilograms of potatoes and 3.48 kilograms of chicken. What is the total weight of the potatoes and chicken combined? Answer: 6.13 Solution: Write the numbers with decimal points aligned: 2.65 and 3.48 Add the hundredths place: 5 + 8 = 13. Write 3 in the hundredths place, carry 1 to the tenths place. Add the tenths place: 6 + 4 + 1 (carried) = 11.
   Full step-by-step solution

   Step 1: Write the numbers with decimal points aligned: 2.65 and 3.48 Step 2: Add the hundredths place: 5 + 8 = 13. Write 3 in the hundredths place, carry 1 to the tenths place. Step 3: Add the tenths place: 6 + 4 + 1 (carried) = 11. Write 1 in the tenths place, carry 1 to the ones place. Step 4: Add the ones place: 2 + 3 + 1 (carried) = 6. Step 5: The total is 6.13 kilograms. The answer is 6.13.

6. What is the value of the digit 7 in 5.78? Answer: 0.7 Solution: Identify the position of the digit 7 in the decimal number 5.78. The digit 7 is in the first position to the right of the decimal point, which is the tenths place.
   Full step-by-step solution

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

7. Olivia is looking at a number line diagram that shows a large rectangle divided into 100 equal smaller squares. The first 3 full columns (each column has 10 squares) are shaded, and then 7 additional squares in the next column are shaded. What decimal does the shaded part of the diagram represent? Answer: 0.37 Solution: The large rectangle is divided into 100 equal small squares, so the whole represents 1. Each column of 10 squares is 1 tenth, or 0.1. 3 full columns shaded = 3 × 0.1 = 0.3.
   Full step-by-step solution

   Step 1: The large rectangle is divided into 100 equal small squares, so the whole represents 1. Step 2: Each column of 10 squares is 1 tenth, or 0.1. Step 3: 3 full columns shaded = 3 × 0.1 = 0.3. Step 4: 7 additional squares shaded = 7 hundredths = 0.07. Step 5: Add the tenths and hundredths: 0.3 + 0.07 = 0.37. The shaded part represents the decimal 0.37.

8. Noah is looking at a large square grid that is divided into 100 equal smaller squares. 72 of the small squares are shaded blue. What decimal represents the shaded part of the grid? Answer: 0.72 Solution: The grid is divided into 100 equal parts, so each small square represents 1 hundredth (0.01) of the whole grid. 72 squares are shaded, so the shaded part is 72 hundredths. Write 72 hundredths as a decimal: 0.72.
   Full step-by-step solution

   Step 1: The grid is divided into 100 equal parts, so each small square represents 1 hundredth (0.01) of the whole grid. Step 2: 72 squares are shaded, so the shaded part is 72 hundredths. Step 3: Write 72 hundredths as a decimal: 0.72. The answer is 0.72.

9. 2.75 + 1.50 = ? Answer: 4.25 Solution: Write the numbers vertically, aligning the decimal points. 2.75 + 1.50 Add the hundredths place: 5 + 0 = 5 Add the tenths place: 7 + 5 = 12. Write down 2 and carry over 1 to the ones place.
   Full step-by-step solution

   Step 1: Write the numbers vertically, aligning the decimal points. 2.75 + 1.50 ------- Step 2: Add the hundredths place: 5 + 0 = 5 Step 3: Add the tenths place: 7 + 5 = 12. Write down 2 and carry over 1 to the ones place. Step 4: Add the ones place: 2 + 1 + 1 (carried over) = 4 Step 5: Bring down the decimal point. Step 6: The final answer is 4.25