Place Value Decimals

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Answer Key & Explanations

Place Value Decimals · Grade 5 · Worksheet 3

1. A rectangular prism is drawn on grid paper with a length of 12.5 cm, a width of 8.25 cm, and a height of 6.75 cm. What is the volume of this prism in cubic centimeters? Answer: 696.09375 Solution: Write down the formula for the volume of a rectangular prism: Volume = length × width × height. Substitute the given values into the formula: Volume = 12.5 × 8.25 × 6.75.
   Full step-by-step solution

   Step 1: Write down the formula for the volume of a rectangular prism: Volume = length × width × height. Step 2: Substitute the given values into the formula: Volume = 12.5 × 8.25 × 6.75. Step 3: First, multiply the length and width: 12.5 × 8.25. 12.5 × 8 = 100 12.5 × 0.25 = 3.125 100 + 3.125 = 103.125 Step 4: Now multiply this result by the height: 103.125 × 6.75. 103.125 × 6 = 618.75 103.125 × 0.75 = 77.34375 618.75 + 77.34375 = 696.09375 Step 5: The final volume is 696.09375 cubic centimeters.

2. Matiu is measuring the mass of different metals for a science project. He has a copper strip with a mass of 2.468 kilograms, a zinc strip with a mass of 1.732 kilograms, and a tin strip with a mass of 0.804 kilograms. What is the digit in the thousandths place of the total mass of all three metal strips combined? Answer: 4 Solution: 2.468 1.732 + 0.804 Add the thousandths place: 8 + 2 + 4 = 14. Write 4, carry 1 to the hundredths place. Add the hundredths place: 6 + 3 + 0 + 1 (carried) = 10.
   Full step-by-step solution

   Step 1: Write the numbers with decimal points aligned: 2.468 1.732 + 0.804 -------- Step 2: Add the thousandths place: 8 + 2 + 4 = 14. Write 4, carry 1 to the hundredths place. Step 3: Add the hundredths place: 6 + 3 + 0 + 1 (carried) = 10. Write 0, carry 1 to the tenths place. Step 4: Add the tenths place: 4 + 7 + 8 + 1 (carried) = 20. Write 0, carry 2 to the ones place. Step 5: Add the ones place: 2 + 1 + 0 + 2 (carried) = 5. Write 5. Step 6: Place the decimal point. The total mass is 5.004 kilograms. Step 7: The thousandths place is the third digit after the decimal point. In 5.004, the digits after the decimal are 0 (tenths), 0 (hundredths), 4 (thousandths). The digit in the thousandths place is 4. The answer is 4.

3. Liam is measuring the thickness of different sheets of paper for a science project. He finds that one sheet is 0.125 inches thick, another is 0.375 inches thick, and a third is 0.250 inches thick. If he stacks all three sheets together, what is the total thickness of the stack in inches? Answer: 0.750 Solution: Write down the thicknesses of each sheet. Sheet 1: 0.125 inches Sheet 2: 0.375 inches Sheet 3: 0.250 inches Align the decimal points and add them together.
   Full step-by-step solution

   Let's add the thicknesses of the three sheets step by step. Step 1: Write down the thicknesses of each sheet. Sheet 1: 0.125 inches Sheet 2: 0.375 inches Sheet 3: 0.250 inches Step 2: Align the decimal points and add them together. We can add them in any order since addition is commutative. 0.125 0.375 0.250 Step 3: Start adding from the rightmost column (thousandths place). 0.125 + 0.375 = 0.500 Then add 0.500 + 0.250 = 0.750 Alternatively, add all at once: 0.125 + 0.375 = 0.500 0.500 + 0.250 = 0.750 Step 4: Check the result. 0.125 + 0.375 + 0.250 = 0.750 inches. So, the total thickness of the stack is 0.750 inches.

4. Matiu is looking at a large number line drawn on the classroom wall. The number line goes from 0 to 1 and is divided into 1000 equal segments. He sees a point marked at 0.628. What digit is in the thousandths place of the decimal 0.628? Answer: 8 Solution: Write the decimal: 0.628. Step 2: Identify each digit's place value. The first digit after the decimal is 6, which is in the tenths place.
   Full step-by-step solution

   Step 1: Write the decimal: 0.628. Step 2: Identify each digit's place value. The first digit after the decimal is 6, which is in the tenths place. The second digit is 2, which is in the hundredths place. The third digit is 8, which is in the thousandths place. Step 3: The digit in the thousandths place is 8. The answer is 8.

5. Liam is measuring the mass of different fruits for a science experiment. He places a small apple on a digital scale, and it shows 0.250 kilograms. He then adds a pear that weighs 0.125 kilograms more than the apple. Finally, he adds a bunch of grapes that weighs 0.375 kilograms. What is the total mass of all the fruit on the scale in kilograms? Answer: 1.000 Solution: The apple's mass is 0.250 kg. The pear weighs 0.125 kg more, so the pear's mass is 0.250 + 0.125 = 0.375 kg. Step 2: Now add the three masses: apple (0.250), pear (0.375), and grapes (0.375).
   Full step-by-step solution

   Step 1: The apple's mass is 0.250 kg. The pear weighs 0.125 kg more, so the pear's mass is 0.250 + 0.125 = 0.375 kg. Step 2: Now add the three masses: apple (0.250), pear (0.375), and grapes (0.375). Step 3: Write them with aligned decimal points: 0.250 0.375 + 0.375 -------- Step 4: Add thousandths: 0 + 5 + 5 = 10, write 0 and carry 1 to hundredths. Step 5: Add hundredths: 5 + 7 + 7 + 1 (carried) = 20, write 0 and carry 2 to tenths. Step 6: Add tenths: 2 + 3 + 3 + 2 (carried) = 10, write 0 and carry 1 to ones. Step 7: Add ones: 0 + 0 + 0 + 1 (carried) = 1. Step 8: The total mass is 1.000 kg. The answer is 1.000.

6. Olivia is measuring the thickness of different layers in a geology project. She measures a layer of sandstone at 0.625 inches, a layer of limestone at 0.875 inches, and a layer of shale at 0.250 inches. If she stacks all three layers together, what is the total thickness of the stack in inches? Answer: 1.750 Solution: Write the three thicknesses with aligned decimal points: 0.625, 0.875, and 0.250. Add the thousandths place: 5 + 5 + 0 = 10. Write 0, carry 1 to the hundredths place.
   Full step-by-step solution

   Step 1: Write the three thicknesses with aligned decimal points: 0.625, 0.875, and 0.250. Step 2: Add the thousandths place: 5 + 5 + 0 = 10. Write 0, carry 1 to the hundredths place. Step 3: Add the hundredths place: 2 + 7 + 5 + 1 (carried) = 15. Write 5, carry 1 to the tenths place. Step 4: Add the tenths place: 6 + 8 + 2 + 1 (carried) = 17. Write 7, carry 1 to the ones place. Step 5: Add the ones place: 0 + 0 + 0 + 1 (carried) = 1. Write 1. Step 6: The total is 1.750 inches. The answer is 1.750.