Place Value Decimals

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Place Value Decimals · Grade 5 · Worksheet 2

1. Noah is measuring the mass of different gemstones for his geology collection. He finds that a quartz crystal has a mass of 8.375 grams, an amethyst has a mass of 7.942 grams, and a garnet has a mass of 9.683 grams. What is the total mass of all three gemstones in grams? Answer: 26.000 Solution: Write the three masses lined up by decimal point: 8.375, 7.942, and 9.683 Add the thousandths place: 5 + 2 + 3 = 10, write 0 and carry 1 Add the hundredths place: 7 + 4 + 8 + 1 (carried) = 20, write 0 and carry 2 Add the tenths place: 3 + 9 + 6 + 2 (carried) = 20, write 0 and carry 2 Add the…
   Full step-by-step solution

   Step 1: Write the three masses lined up by decimal point: 8.375, 7.942, and 9.683 Step 2: Add the thousandths place: 5 + 2 + 3 = 10, write 0 and carry 1 Step 3: Add the hundredths place: 7 + 4 + 8 + 1 (carried) = 20, write 0 and carry 2 Step 4: Add the tenths place: 3 + 9 + 6 + 2 (carried) = 20, write 0 and carry 2 Step 5: Add the ones place: 8 + 7 + 9 + 2 (carried) = 26 Step 6: The total mass is 26.000 grams The answer is 26.000.

2. What is the value of the digit 4 in the number 6.824? Answer: 0.004 Solution: Write the number 6.824 and label each digit's place value. 6 is in the ones place. 8 is in the tenths place (0.8).
   Full step-by-step solution

   Step 1: Write the number 6.824 and label each digit's place value. 6 is in the ones place. 8 is in the tenths place (0.8). 2 is in the hundredths place (0.02). 4 is in the thousandths place (0.004). Step 2: The digit 4 is in the thousandths place, so its value is 4 thousandths, written as 0.004. The answer is 0.004.

3. 7.345 + 2.678 = ? Answer: 10.023 Solution: Write the numbers one under the other, aligning the decimal points. 7.345 + 2.678 Add the digits in the thousandths place (the third digit after the decimal). 5 (thousandths) + 8 (thousandths) = 13 thousandths.
   Full step-by-step solution

   Let's add 7.345 and 2.678 step by step. Step 1: Write the numbers one under the other, aligning the decimal points. 7.345 + 2.678 --------- Step 2: Add the digits in the thousandths place (the third digit after the decimal). 5 (thousandths) + 8 (thousandths) = 13 thousandths. Write down the 3 in the thousandths place, and carry over the 1 to the hundredths place. Interim result: ... .??3 Carry: 1 Step 3: Add the digits in the hundredths place (the second digit after the decimal), including the carry. 4 (hundredths) + 7 (hundredths) = 11 hundredths, plus the carried 1 makes 12 hundredths. Write down the 2 in the hundredths place, and carry over the 1 to the tenths place. Interim result: ... .?23 Carry: 1 Step 4: Add the digits in the tenths place (the first digit after the decimal), including the carry. 3 (tenths) + 6 (tenths) = 9 tenths, plus the carried 1 makes 10 tenths. Write down the 0 in the tenths place, and carry over the 1 to the units (ones) place. Interim result: ... .023 Carry: 1 Step 5: Add the digits in the units place (the ones place). 7 (ones) + 2 (ones) = 9 ones, plus the carried 1 makes 10 ones. Write down the 0 in the ones place, and carry over the 1 to the tens place. Interim result: 10.023 Carry: 1 (to tens place, but there are no more digits, so it becomes the tens digit). Step 6: Write the final number. The tens digit is 1, the ones digit is 0, then decimal point, then tenths 0, hundredths 2, thousandths 3. Final answer: 10.023

4. 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

5. Mason is measuring the mass of different ingredients for a baking science experiment. He measures 2.147 kilograms of flour, 1.032 kilograms of sugar, and 0.725 kilograms of butter. What is the digit in the thousandths place of the total mass of all three ingredients combined? Answer: 4 Solution: 2.147 1.032 + 0.725 Add the thousandths place: 7 + 2 + 5 = 14. Write 4, carry over 1 to the hundredths place. Add the hundredths place: 4 + 3 + 2 + 1 (carried) = 10.
   Full step-by-step solution

   Step 1: Write the three masses lined up by decimal point: 2.147 1.032 + 0.725 -------- 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: 4 + 3 + 2 + 1 (carried) = 10. Write 0, carry over 1 to the tenths place. Step 4: Add the tenths place: 1 + 0 + 7 + 1 (carried) = 9. Write 9. Step 5: Add the ones place: 2 + 1 + 0 = 3. Step 6: The total mass is 3.904 kilograms. Step 7: The digit in the thousandths place (third digit after the decimal) is 4. The answer is 4.

6. Emma is designing a mosaic art project using small glass tiles. She measures the thickness of three different tile types: the clear tiles are 0.125 inches thick, the colored tiles are 0.375 inches thick, and the metallic tiles are 0.250 inches thick. If Emma creates a pattern using one of each tile type stacked together, what is the total thickness of her tile stack in inches? Answer: 0.750 Solution: Clear tiles: 0.125 inches Colored tiles: 0.375 inches Metallic tiles: 0.250 inches Set up the addition problem by aligning the decimal points: 0.125 0.375 + 0.250 Add the thousandths place: 5 + 5 + 0 = 10 thousandths Write 0 in the thousandths place, carry 1 to the hundredths place Add the…
   Full step-by-step solution

   Step 1: Write down the thickness of each tile type: Clear tiles: 0.125 inches Colored tiles: 0.375 inches Metallic tiles: 0.250 inches Step 2: Set up the addition problem by aligning the decimal points: 0.125 0.375 + 0.250 Step 3: Add the thousandths place: 5 + 5 + 0 = 10 thousandths Write 0 in the thousandths place, carry 1 to the hundredths place Step 4: Add the hundredths place: 2 + 7 + 5 + 1 (carried) = 15 hundredths Write 5 in the hundredths place, carry 1 to the tenths place Step 5: Add the tenths place: 1 + 3 + 2 + 1 (carried) = 7 tenths Write 7 in the tenths place Step 6: Add the ones place: 0 + 0 + 0 = 0 Step 7: The total thickness is 0.750 inches Answer: 0.750

7. What is the value of the digit 7 in the number 5.937? Answer: 0.007 Solution: Look at the number 5.937. The digits after the decimal point are 9, 3, and 7. The first digit after the decimal (9) is in the tenths place, so its value is 9/10 or 0.9.
   Full step-by-step solution

   Step 1: Look at the number 5.937. The digits after the decimal point are 9, 3, and 7. Step 2: The first digit after the decimal (9) is in the tenths place, so its value is 9/10 or 0.9. Step 3: The second digit (3) is in the hundredths place, so its value is 3/100 or 0.03. Step 4: The third digit (7) is in the thousandths place, so its value is 7/1000 or 0.007. Step 5: Therefore, the value of the digit 7 in 5.937 is 0.007. The answer is 0.007.

8. Liam is measuring the thickness of five different sheets of paper for his science project. The measurements are 0.125 inches, 0.250 inches, 0.375 inches, 0.062 inches, and 0.188 inches. What is the total thickness in inches if he stacks all five sheets together? Answer: 1.000 Solution: 0.125, 0.250, 0.375, 0.062, 0.188 0.125 + 0.250 = 0.375 0.375 (from step 2) + 0.375 = 0.750 0.750 + 0.062 = 0.812 0.812 + 0.188 = 1.000 Check the reasoning — these are decimal inches, and adding carefully gives exactly 1.000 inches.
   Full step-by-step solution

   Let's add the thicknesses step by step. Step 1: Write down all measurements: 0.125, 0.250, 0.375, 0.062, 0.188 Step 2: Add the first two: 0.125 + 0.250 = 0.375 Step 3: Add the third measurement: 0.375 (from step 2) + 0.375 = 0.750 Step 4: Add the fourth measurement: 0.750 + 0.062 = 0.812 Step 5: Add the fifth measurement: 0.812 + 0.188 = 1.000 Step 6: Check the reasoning — these are decimal inches, and adding carefully gives exactly 1.000 inches. Final answer: 1.000