Decimal Notation

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Answer Key & Explanations

Decimal Notation · Grade 4 · Worksheet 3

1. Emma is baking cookies for a school bake sale. She has 2.75 kilograms of flour. Her cookie recipe requires 0.45 kilograms of flour for one batch. How many kilograms of flour will Emma have left after baking one batch of cookies? Answer: 2.30 Solution: Start with the total amount of flour: 2.75 kg Subtract the flour used for one batch: 2.75 - 0.45 Align the decimal points and subtract: 2.75 - 0.45 = 2.30 The answer is 2.30 kilograms of flour remaining.
   Full step-by-step solution

   Step 1: Start with the total amount of flour: 2.75 kg Step 2: Subtract the flour used for one batch: 2.75 - 0.45 Step 3: Align the decimal points and subtract: 2.75 - 0.45 = 2.30 Step 4: The answer is 2.30 kilograms of flour remaining.

2. Kaia is helping her aunt organize a community garden. They have a large bag of soil that weighs 45.78 kilograms. Kaia's aunt asks her to write down the weight of the soil in expanded form, showing the value of each digit. How should Kaia write 45.78 in expanded form? Answer: 40 + 5 + 0.7 + 0.08 Solution: Identify the place value of each digit in 45.78. The digit 4 is in the tens place, so it represents 40. The digit 5 is in the ones place, so it represents 5.
   Full step-by-step solution

   Step 1: Identify the place value of each digit in 45.78. The digit 4 is in the tens place, so it represents 40. The digit 5 is in the ones place, so it represents 5. The digit 7 is in the tenths place, so it represents 0.7 (or 7/10). The digit 8 is in the hundredths place, so it represents 0.08 (or 8/100). Step 2: Write the number as the sum of these values: 40 + 5 + 0.7 + 0.08. Step 3: Check: 40 + 5 = 45, and 0.7 + 0.08 = 0.78, so 45 + 0.78 = 45.78. The expanded form of 45.78 is 40 + 5 + 0.7 + 0.08.

3. Olivia is measuring ingredients for a science experiment. She needs 4.35 liters of water for one part of the experiment and 2.65 liters of water for another part. How many liters of water does Olivia need in total? Answer: 7.00 Solution: Write the amounts with decimal points lined up: 4.35 and 2.65. Add the hundredths place: 5 hundredths + 5 hundredths = 10 hundredths. Write 0 in the hundredths place and carry 1 to the tenths place.
   Full step-by-step solution

   Step 1: Write the amounts with decimal points lined up: 4.35 and 2.65. Step 2: Add the hundredths place: 5 hundredths + 5 hundredths = 10 hundredths. Write 0 in the hundredths place and carry 1 to the tenths place. Step 3: Add the tenths place: 3 tenths + 6 tenths + 1 carried tenth = 10 tenths. Write 0 in the tenths place and carry 1 to the ones place. Step 4: Add the ones place: 4 ones + 2 ones + 1 carried one = 7 ones. Step 5: Combine all places: 7 ones, 0 tenths, 0 hundredths = 7.00. Olivia needs 7.00 liters of water in total.

4. Liam is measuring ribbon for a craft project. He has a piece that is 2.75 meters long. He cuts off 0.45 meters to use for a bow. How many meters of ribbon does Liam have left? Answer: 2.30 Solution: Liam starts with a ribbon that is 2.75 meters long. He cuts off 0.45 meters for a bow. To find how much ribbon is left, subtract the length he cut from the original length.
   Full step-by-step solution

   Liam starts with a ribbon that is 2.75 meters long. He cuts off 0.45 meters for a bow. To find how much ribbon is left, subtract the length he cut from the original length. Step 1: Write the subtraction. 2.75 - 0.45 Step 2: Subtract the hundredths place first. 5 hundredths - 5 hundredths = 0 hundredths. Write 0 in the hundredths place. Step 3: Subtract the tenths place. 7 tenths - 4 tenths = 3 tenths. Write 3 in the tenths place. Step 4: Subtract the ones place. 2 ones - 0 ones = 2 ones. Write 2 in the ones place. Step 5: Combine the results. The result is 2.30 meters. So, Liam has 2.30 meters of ribbon left.

5. Liam is helping his mom measure ingredients for a large batch of lemonade. The recipe calls for 3.75 liters of water and 1.25 liters of lemon juice. How many liters of liquid are in the lemonade mixture in total? Answer: 5.00 Solution: Write the two amounts with decimal points aligned: 3.75 and 1.25. Add the hundredths place: 5 + 5 = 10. Write 0 in the hundredths place, carry 1 to the tenths place.
   Full step-by-step solution

   Step 1: Write the two amounts with decimal points aligned: 3.75 and 1.25. Step 2: Add the hundredths place: 5 + 5 = 10. Write 0 in the hundredths place, carry 1 to the tenths place. Step 3: Add the tenths place: 7 + 2 + 1 (carried) = 10. Write 0 in the tenths place, carry 1 to the ones place. Step 4: Add the ones place: 3 + 1 + 1 (carried) = 5. Step 5: The decimal point stays in the same place, so the total is 5.00 liters. The answer is 5.00.

6. Liam is building a rectangular garden bed that is 3.5 meters long and 2.25 meters wide. He wants to put a decorative border around the entire garden. How many meters of border does Liam need to buy? Answer: 11.5 Solution: To find how many meters of border Liam needs, we need to calculate the perimeter of the rectangular garden bed. Identify the formula for the perimeter of a rectangle. P = 2 * (length + width) Write down the given measurements.
   Full step-by-step solution

   To find how many meters of border Liam needs, we need to calculate the perimeter of the rectangular garden bed. Step 1: Identify the formula for the perimeter of a rectangle. The perimeter P of a rectangle is given by: P = 2 * (length + width) Step 2: Write down the given measurements. Length = 3.5 meters Width = 2.25 meters Step 3: Substitute the values into the formula. P = 2 * (3.5 + 2.25) Step 4: Perform the addition inside the parentheses. 3.5 + 2.25 = 5.75 Step 5: Multiply the result by 2. P = 2 * 5.75 P = 11.5 Step 6: State the final answer. Liam needs to buy 11.5 meters of border.

7. 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.