Place Value Decimals

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Answer Key & Explanations

Place Value Decimals · Grade 5 · Worksheet 1

1. Kaia is helping her mother measure ingredients for a new bread recipe. The recipe calls for 0.785 kilograms of whole wheat flour and 0.218 kilograms of white flour. What is the total weight of flour Kaia needs in kilograms? Answer: 1.003 Solution: Write the two decimal numbers with decimal points aligned: 0.785 + 0.218 Add the thousandths place (rightmost column): 5 + 8 = 13. Write 3 in the thousandths place, carry 1 to the hundredths place.
   Full step-by-step solution

   Step 1: Write the two decimal numbers with decimal points aligned: 0.785 + 0.218 Step 2: Add the thousandths place (rightmost column): 5 + 8 = 13. Write 3 in the thousandths place, carry 1 to the hundredths place. Step 3: Add the hundredths place: 8 + 1 + 1 (carried) = 10. Write 0 in the hundredths place, carry 1 to the tenths place. Step 4: Add the tenths place: 7 + 2 + 1 (carried) = 10. Write 0 in the tenths place, carry 1 to the ones place. Step 5: Add the ones place: 0 + 0 + 1 (carried) = 1. Write 1 in the ones place. Step 6: The total is 1.003 kilograms. The answer is 1.003.

2. A rectangular prism is built using centimeter cubes. The prism has a length of 12 cubes, a width of 8 cubes, and a height of 5 cubes. What is the total volume of the prism in cubic centimeters? Answer: 480 Solution: We have a rectangular prism made of centimeter cubes. Each cube has a volume of 1 cubic centimeter. The prism's dimensions in cubes are: Length = 12 cubes, Width = 8 cubes, Height = 5 cubes.
   Full step-by-step solution

   Step 1: Understand the problem. We have a rectangular prism made of centimeter cubes. Each cube has a volume of 1 cubic centimeter. The prism's dimensions in cubes are: Length = 12 cubes, Width = 8 cubes, Height = 5 cubes. Step 2: Recall the volume formula for a rectangular prism. Volume = Length × Width × Height. Step 3: Substitute the given dimensions into the formula. Volume = 12 × 8 × 5. Step 4: Perform the multiplication step by step. First, multiply 12 and 8: 12 × 8 = 96. Step 5: Multiply the result by the height: 96 × 5 = 480. Step 6: State the final answer with units. Since each cube is 1 cubic centimeter, the total volume is 480 cubic centimeters. Final answer: 480

3. Emma is measuring the thickness of different coins for her math project. She finds that a penny is 0.059 inches thick, a nickel is 0.077 inches thick, and a dime is 0.053 inches thick. If Emma stacks one of each coin together, what is the total thickness of the stack in inches? Answer: 0.189 Solution: Penny: 0.059 inches Nickel: 0.077 inches Dime: 0.053 inches 0.059 + 0.077 + 0.053 Add thousandths place: 9 + 7 + 3 = 19 (write 9, carry 1) Add hundredths place: 5 + 7 + 5 + 1 (carried) = 18 (write 8, carry 1) Add tenths place: 0 + 0 + 0 + 1 (carried) = 1 The total is 0.189 inches The answer is…
   Full step-by-step solution

   Step 1: Write down the thickness of each coin Penny: 0.059 inches Nickel: 0.077 inches Dime: 0.053 inches Step 2: Align the decimals and add the numbers 0.059 + 0.077 + 0.053 Step 3: Add thousandths place: 9 + 7 + 3 = 19 (write 9, carry 1) Step 4: Add hundredths place: 5 + 7 + 5 + 1 (carried) = 18 (write 8, carry 1) Step 5: Add tenths place: 0 + 0 + 0 + 1 (carried) = 1 Step 6: The total is 0.189 inches The answer is 0.189 inches.

4. 0.375 + 0.624 = ? Answer: 0.999 Solution: Write the numbers aligned by their decimal points in your mind: 0.375 + 0.624 Add the digits in the thousandths place (third decimal place): 5 (thousandths) + 4 (thousandths) = 9 thousandths.
   Full step-by-step solution

   Let's add 0.375 and 0.624 step by step. Step 1: Write the numbers aligned by their decimal points in your mind: 0.375 + 0.624 Step 2: Add the digits in the thousandths place (third decimal place): 5 (thousandths) + 4 (thousandths) = 9 thousandths. So, the thousandths place of the result is 9. Step 3: Add the digits in the hundredths place (second decimal place): 7 (hundredths) + 2 (hundredths) = 9 hundredths. So, the hundredths place of the result is 9. Step 4: Add the digits in the tenths place (first decimal place): 3 (tenths) + 6 (tenths) = 9 tenths. So, the tenths place of the result is 9. Step 5: Add the whole number parts: 0 + 0 = 0. Step 6: Combine the whole number part and decimal part: 0 . 9 9 9 So, 0.375 + 0.624 = 0.999. We can verify by converting to fractions: 0.375 = 375/1000 = 3/8 0.624 = 624/1000 = 78/125 But adding directly as decimals is simpler here. Final answer: 0.999

5. Liam is measuring the thickness of different sheets of paper for an art 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 Liam stacks all three sheets together, what is the total thickness of the stack in inches? Answer: 0.750 Solution: Sheet 1 = 0.125 inches Sheet 2 = 0.375 inches Sheet 3 = 0.250 inches 0.125 + 0.375 First, add the thousandths: 125 + 375 = 500 thousandths, which is 0.500 inches. So, 0.125 + 0.375 = 0.500.
   Full step-by-step solution

   Let's add the thicknesses step by step. Step 1: Write down the thicknesses of the three sheets: Sheet 1 = 0.125 inches Sheet 2 = 0.375 inches Sheet 3 = 0.250 inches Step 2: Add the first two thicknesses: 0.125 + 0.375 First, add the thousandths: 125 + 375 = 500 thousandths, which is 0.500 inches. So, 0.125 + 0.375 = 0.500. Step 3: Add the third sheet's thickness to the result from Step 2: 0.500 + 0.250 500 thousandths + 250 thousandths = 750 thousandths, which is 0.750 inches. Step 4: Final total: 0.125 + 0.375 + 0.250 = 0.750 inches. Answer: 0.750

6. What is the value of the digit 7 in the number 6.247? Answer: 0.007 Solution: Look at the number 6.247. The digits after the decimal point are 2, 4, and 7. The first digit after the decimal (2) is in the tenths place, worth 0.2.
   Full step-by-step solution

   Step 1: Look at the number 6.247. The digits after the decimal point are 2, 4, and 7. Step 2: The first digit after the decimal (2) is in the tenths place, worth 0.2. Step 3: The second digit (4) is in the hundredths place, worth 0.04. Step 4: The third digit (7) is in the thousandths place, worth 0.007. Step 5: Therefore, the value of the digit 7 is 0.007. The answer is 0.007.

7. A rectangular prism is drawn with a length of 8.5 cm, a width of 6.2 cm, and a height of 4.7 cm. What is the volume of this prism? Answer: 247.69 Solution: To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Write down the given dimensions.
   Full step-by-step solution

   To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Step 1: Write down the given dimensions. Length = 8.5 cm Width = 6.2 cm Height = 4.7 cm Step 2: Substitute the given numbers into the volume formula. Volume = 8.5 × 6.2 × 4.7 Step 3: Perform the multiplication step-by-step. First, multiply the length and the width. 8.5 × 6.2 To do this, we can calculate 85 × 62 and then divide by 100 because each number has one decimal place. 85 × 62 = 85 × (60 + 2) = (85 × 60) + (85 × 2) = 5100 + 170 = 5270 Since we have one decimal place in each of the original numbers (8.5 and 6.2), we need to divide this result by 100. So, 8.5 × 6.2 = 5270 / 100 = 52.70 Step 4: Now multiply this result by the height. 52.70 × 4.7 To do this, we can calculate 5270 × 47 and then divide by 1000. Here's why: 52.70 has two decimal places, and 4.7 has one decimal place, so the total number of decimal places in the final product will be three. 5270 × 47 = 5270 × (40 + 7) = (5270 × 40) + (5270 × 7) = 210800 + 36890 = 247690 Now, since we need three decimal places, we divide by 1000. 247690 / 1000 = 247.690 Step 5: Write the final answer. The volume is 247.69 cubic centimeters (we round to two decimal places, as is standard for this type of measurement). Final Answer: 247.69