Decimal Notation

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Decimal Notation · Grade 4 · Worksheet 2

1. 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.

2. Matiu is helping his grandfather measure timber for a new fence. They need a piece that is 4.35 meters long and another piece that is 2.65 meters long. What is the total length of timber they need in meters? Answer: 7.00 Solution: Write the numbers with decimal points aligned: 4.35 + 2.65. Add the hundredths: 5 + 5 = 10. Write 0 in the hundredths place, carry 1 to the tenths place.
   Full step-by-step solution

   Step 1: Write the numbers with decimal points aligned: 4.35 + 2.65. Step 2: Add the hundredths: 5 + 5 = 10. Write 0 in the hundredths place, carry 1 to the tenths place. Step 3: Add the tenths: 3 + 6 + 1 (carried) = 10. Write 0 in the tenths place, carry 1 to the ones place. Step 4: Add the ones: 4 + 2 + 1 (carried) = 7. Step 5: Write the decimal point in the answer. The total length is 7.00 meters. Answer: 7.00

3. Kaia draws a number line from 0 to 1. She divides the space between 0 and 1 into 10 equal parts and labels the first 7 marks after 0. She then shades the first 5 of those 7 marks. What decimal represents the part of the number line that is shaded? Answer: 0.5 Solution: Each part represents one tenth, or 0.1. Kaia shades the first 5 of those 10 equal parts. The fraction shaded is 5/10.
   Full step-by-step solution

   Step 1: The number line from 0 to 1 is divided into 10 equal parts. Each part represents one tenth, or 0.1. Step 2: Kaia shades the first 5 of those 10 equal parts. Step 3: The fraction shaded is 5/10. Step 4: To write 5/10 as a decimal, note that the 5 is in the tenths place, so it is 0.5. Step 5: The decimal that represents the shaded part is 0.5.

4. Charlotte is helping her dad measure ingredients for a special pancake recipe. The recipe calls for 2.7 cups of buttermilk and 1.2 cups of blueberries. Write the number that represents the total amount of buttermilk and blueberries combined as a decimal. Answer: 3.9 Solution: Write the two amounts with decimal points aligned: 2.7 + 1.2 Add the tenths place: 7 tenths + 2 tenths = 9 tenths. Write 9 in the tenths place. Add the ones place: 2 ones + 1 one = 3 ones.
   Full step-by-step solution

   Step 1: Write the two amounts with decimal points aligned: 2.7 + 1.2 Step 2: Add the tenths place: 7 tenths + 2 tenths = 9 tenths. Write 9 in the tenths place. Step 3: Add the ones place: 2 ones + 1 one = 3 ones. Write 3 in the ones place. Step 4: Place the decimal point in the answer directly below the other decimal points. Step 5: The total is 3.9. The answer is 3.9.

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. 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.

7. Emma is baking cookies for a school bake sale. She needs 0.75 cups of sugar for the chocolate chip cookies and 1.25 cups of sugar for the oatmeal raisin cookies. How many cups of sugar does Emma need in total for both types of cookies? Answer: 2.00 Solution: Identify the amounts of sugar needed: 0.75 cups for chocolate chip cookies and 1.25 cups for oatmeal raisin cookies.
   Full step-by-step solution

   Step 1: Identify the amounts of sugar needed: 0.75 cups for chocolate chip cookies and 1.25 cups for oatmeal raisin cookies. Step 2: Set up the addition problem: 0.75 + 1.25 Step 3: Line up the decimal points and add the hundredths place: 5 + 5 = 10. Write down 0 in the hundredths place and carry over 1 to the tenths place. Step 4: Add the tenths place: 7 + 2 + 1 (carried over) = 10. Write down 0 in the tenths place and carry over 1 to the ones place. Step 5: Add the ones place: 0 + 1 + 1 (carried over) = 2. Write down 2 in the ones place. Step 6: Place the decimal point in the answer: 2.00 Emma needs 2.00 cups of sugar in total.

8. Lily is measuring fabric for a school project. She needs 2.5 meters of blue fabric and 1.75 meters of red fabric. How many meters of fabric does Lily need in total? Answer: 4.25 Solution: Identify the amounts of fabric needed. Lily needs 2.5 meters of blue fabric and 1.75 meters of red fabric. Write the addition expression for the total fabric.
   Full step-by-step solution

   Step 1: Identify the amounts of fabric needed. Lily needs 2.5 meters of blue fabric and 1.75 meters of red fabric. Step 2: Write the addition expression for the total fabric. Total fabric = 2.5 + 1.75 Step 3: Align the decimal points and add the numbers. We can write them one below the other for clarity: 2.50 + 1.75 ------- Step 4: Add the hundredths place: 0 + 5 = 5. Write 5 in the hundredths place. Step 5: Add the tenths place: 5 + 7 = 12. Write 2 in the tenths place, and carry over 1 to the units place. Step 6: Add the units place: 2 + 1 + 1 (carry) = 4. Write 4 in the units place. Step 7: The result is 4.25. Step 8: Final answer: Lily needs 4.25 meters of fabric in total.

9. What is the value of the digit 7 in 5.47? Answer: 0.07 Solution: Identify the position of the digit 7 in the number 5.47. The digit 7 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 7 in the number 5.47. Step 2: The digit 7 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, 7 in the hundredths place means 7/100 = 0.07. The answer is 0.07.