Place Value Decimals

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Answer Key & Explanations

Place Value Decimals · Grade 5 · Worksheet 1

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. 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

3. 0.375 + 0.642 = ? Answer: 1.017 Solution: Write the numbers aligned by their decimal points in your mind: 0.375 + 0.642 Start adding from the rightmost digit (thousandths place). Thousandths place: 5 + 2 = 7 Write 7 in the thousandths place.
   Full step-by-step solution

   Let's add 0.375 and 0.642 step by step. Step 1: Write the numbers aligned by their decimal points in your mind: 0.375 + 0.642 Step 2: Start adding from the rightmost digit (thousandths place). Thousandths place: 5 + 2 = 7 Write 7 in the thousandths place. Step 3: Move left to the hundredths place: 7 + 4 = 11 Write 1 in the hundredths place, and carry over 1 to the tenths place. Step 4: Tenths place: 3 + 6 = 9, plus the carried-over 1 = 10 Write 0 in the tenths place, and carry over 1 to the ones place. Step 5: Ones place: 0 + 0 = 0, plus the carried-over 1 = 1 Write 1 in the ones place. Step 6: Combine all digits: Ones place: 1 Tenths place: 0 Hundredths place: 1 Thousandths place: 7 So the result is 1.017. Final answer: 1.017

4. 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

5. Olivia is measuring the mass of different fruits for a science experiment. She finds that a strawberry has a mass of 0.025 kilograms, a blueberry has a mass of 0.010 kilograms, and a raspberry has a mass of 0.015 kilograms. What is the total mass of all three fruits combined in kilograms? Answer: 0.050 Solution: Write the three masses to add: 0.025, 0.010, and 0.015 0.025 0.010 + 0.015 Add the thousandths place: 5 + 0 + 5 = 10 (write 0, carry over 1) Add the hundredths place: 2 + 1 + 1 + 1 (carried) = 5 (write 5) Add the tenths place: 0 + 0 + 0 = 0 (write 0) Add the ones place: 0 + 0 + 0 = 0 (write 0)…
   Full step-by-step solution

   Step 1: Write the three masses to add: 0.025, 0.010, and 0.015 Step 2: Align the decimal points and add: 0.025 0.010 + 0.015 -------- Step 3: Add the thousandths place: 5 + 0 + 5 = 10 (write 0, carry over 1) Step 4: Add the hundredths place: 2 + 1 + 1 + 1 (carried) = 5 (write 5) Step 5: Add the tenths place: 0 + 0 + 0 = 0 (write 0) Step 6: Add the ones place: 0 + 0 + 0 = 0 (write 0) Step 7: The total mass is 0.050 kilograms The answer is 0.050.

6. 0.375 + 0.249 = ? Answer: 0.624 Solution: Write the numbers aligned by their decimal points for clarity in our thinking. 0.375 0.249 Add the digits in the thousandths place (third decimal place). 5 thousandths + 9 thousandths = 14 thousandths.
   Full step-by-step solution

   Let's add 0.375 and 0.249 step by step. Step 1: Write the numbers aligned by their decimal points for clarity in our thinking. 0.375 0.249 Step 2: Add the digits in the thousandths place (third decimal place). 5 thousandths + 9 thousandths = 14 thousandths. 14 thousandths means 10 thousandths = 1 hundredth, and 4 thousandths left over. So, write down 4 in the thousandths place, and carry over 1 to the hundredths place. Step 3: Add the hundredths place digits, including the carry-over. 7 hundredths + 4 hundredths = 11 hundredths, plus the 1 hundredth carried over = 12 hundredths. 12 hundredths means 10 hundredths = 1 tenth, and 2 hundredths left over. So, write down 2 in the hundredths place, and carry over 1 to the tenths place. Step 4: Add the tenths place digits, including the carry-over. 3 tenths + 2 tenths = 5 tenths, plus the 1 tenth carried over = 6 tenths. Write down 6 in the tenths place. Step 5: Add the whole number parts (to the left of the decimal). 0 + 0 = 0. Step 6: Combine all parts: 0 (whole number) . 6 (tenths) 2 (hundredths) 4 (thousandths) = 0.624. Thus, 0.375 + 0.249 = 0.624.