Place Value Decimals

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Answer Key & Explanations

Place Value Decimals · Grade 5 · Worksheet 3

1. What is the value of the digit 5 in the number 8.205? Answer: 0.005 Solution: Write the number 8.205 and label each digit's place value: 8 is in the ones place, 2 is in the tenths place, 0 is in the hundredths place, and 5 is in the thousandths place.
   Full step-by-step solution

   Step 1: Write the number 8.205 and label each digit's place value: 8 is in the ones place, 2 is in the tenths place, 0 is in the hundredths place, and 5 is in the thousandths place. Step 2: The digit 5 is in the thousandths place, which means its value is 5 × 0.001. Step 3: Multiply: 5 × 0.001 = 0.005. The answer is 0.005.

2. A rectangular prism is drawn with a length of 15.25 cm, a width of 8.4 cm, and a height of 5.75 cm. What is the volume of this prism in cubic centimeters? Answer: 736.575 Solution: Write the formula for the volume of a rectangular prism: Volume = length × width × height Substitute the given values: Volume = 15.25 × 8.4 × 5.75 First multiply 15.25 × 8.4 15.25 × 8 = 122 15.25 × 0.4 = 6.1 122 + 6.1 = 128.1 Now multiply 128.1 × 5.75 128.1 × 5 = 640.5 128.1 × 0.7 = 89.67 128.1…
   Full step-by-step solution

   Step 1: Write the formula for the volume of a rectangular prism: Volume = length × width × height Step 2: Substitute the given values: Volume = 15.25 × 8.4 × 5.75 Step 3: First multiply 15.25 × 8.4 15.25 × 8 = 122 15.25 × 0.4 = 6.1 122 + 6.1 = 128.1 Step 4: Now multiply 128.1 × 5.75 128.1 × 5 = 640.5 128.1 × 0.7 = 89.67 128.1 × 0.05 = 6.405 640.5 + 89.67 = 730.17 730.17 + 6.405 = 736.575 Step 5: The volume is 736.575 cubic centimeters.

3. Write 9.847 in expanded form. Answer: 9 + 0.8 + 0.04 + 0.007 Solution: Identify the place value of each digit in 9.847.
   Full step-by-step solution

   Step 1: Identify the place value of each digit in 9.847. - The digit 9 is in the ones place: 9 × 1 = 9 - The digit 8 is in the tenths place: 8 × 0.1 = 0.8 - The digit 4 is in the hundredths place: 4 × 0.01 = 0.04 - The digit 7 is in the thousandths place: 7 × 0.001 = 0.007 Step 2: Write the sum of these values: 9 + 0.8 + 0.04 + 0.007 The answer is 9 + 0.8 + 0.04 + 0.007.

4. 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.

5. 0.456 × 0.75 = ? Answer: 0.342 Solution: Multiply the numbers as if they were whole numbers: 456 × 75. Calculate 456 × 75 = 456 × (70 + 5) = (456 × 70) + (456 × 5) = 31920 + 2280 = 34200.
   Full step-by-step solution

   Step 1: Multiply the numbers as if they were whole numbers: 456 × 75. Step 2: Calculate 456 × 75 = 456 × (70 + 5) = (456 × 70) + (456 × 5) = 31920 + 2280 = 34200. Step 3: Count the total decimal places in the original factors: 0.456 has 3 decimal places, and 0.75 has 2 decimal places, so the total is 3 + 2 = 5 decimal places. Step 4: Place the decimal point in the product (34200) so that it has 5 decimal places: 0.34200. Step 5: Simplify by removing the trailing zeros: 0.34200 becomes 0.342. The answer is 0.342.

6. What is the value of the digit 7 in the number 9.317? Answer: 0.007 Solution: Look at the number 9.317. The digits after the decimal point are 3, 1, and 7.
   Full step-by-step solution

   Step 1: Look at the number 9.317. The digits after the decimal point are 3, 1, and 7. Step 2: Identify the place value of each digit: - The 3 is in the tenths place (0.3) - The 1 is in the hundredths place (0.01) - The 7 is in the thousandths place (0.001) Step 3: The digit 7 is in the thousandths place, so its value is 7 × 0.001 = 0.007. The answer is 0.007.

7. Mason is measuring the mass of different seeds for a science experiment. A sunflower seed has a mass of 0.127 grams, a pumpkin seed has a mass of 0.352 grams, and a watermelon seed has a mass of 0.215 grams. What is the total mass of all three seeds combined in grams? Answer: 0.694 Solution: Write the three masses with aligned decimal points: 0.127 0.352 + 0.215 Add the thousandths place: 7 + 2 + 5 = 14. Write 4, carry over 1 to the hundredths place. Add the hundredths place: 2 + 5 + 1 + 1 (carried) = 9.
   Full step-by-step solution

   Step 1: Write the three masses with aligned decimal points: 0.127 0.352 + 0.215 -------- Step 2: Add the thousandths place: 7 + 2 + 5 = 14. Write 4, carry over 1 to the hundredths place. Step 3: Add the hundredths place: 2 + 5 + 1 + 1 (carried) = 9. Write 9. Step 4: Add the tenths place: 1 + 3 + 2 = 6. Write 6. Step 5: Add the ones place: 0 + 0 + 0 = 0. Write 0. Step 6: The total is 0.694 grams. The answer is 0.694.