Decimal Operations

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Answer Key & Explanations

Decimal Operations · Grade 5 · Worksheet 2

1. 3.75 + 2.125 = ? Answer: 5.875 Solution: 3.750 + 2.125 Add the thousandths place: 0 + 5 = 5 Add the hundredths place: 5 + 2 = 7 Add the tenths place: 7 + 1 = 8 Add the ones place: 3 + 2 = 5 Combine all place values: 5.875 The answer is 5.875.
   Full step-by-step solution

   Step 1: Write the numbers with aligned decimal points: 3.750 + 2.125 Step 2: Add the thousandths place: 0 + 5 = 5 Step 3: Add the hundredths place: 5 + 2 = 7 Step 4: Add the tenths place: 7 + 1 = 8 Step 5: Add the ones place: 3 + 2 = 5 Step 6: Combine all place values: 5.875 The answer is 5.875.

2. Olivia is comparing the distances she ran over three days. On Monday, she ran 3.405 kilometers. On Tuesday, she ran 3.45 kilometers. On Wednesday, she ran 3.455 kilometers. Which day did Olivia run the farthest? Answer: Wednesday Solution: Write all distances with the same number of decimal places (thousandths): Monday: 3.405 km, Tuesday: 3.450 km, Wednesday: 3.455 km. Compare the whole number part (ones place): All have 3, so move to tenths.
   Full step-by-step solution

   Step 1: Write all distances with the same number of decimal places (thousandths): Monday: 3.405 km, Tuesday: 3.450 km, Wednesday: 3.455 km. Step 2: Compare the whole number part (ones place): All have 3, so move to tenths. Step 3: Compare tenths: All have 4, so move to hundredths. Step 4: Compare hundredths: Monday has 0, Tuesday has 5, Wednesday has 5. Monday is smaller, so it is not the farthest. Step 5: Compare thousandths for Tuesday and Wednesday: Tuesday has 0, Wednesday has 5. 5 is greater than 0, so 3.455 km is the largest. Step 6: Olivia ran the farthest on Wednesday with 3.455 kilometers. The answer is Wednesday.

3. Sophia is training for a science competition where she needs to measure and compare the masses of different soil samples. She has three samples: Sample A has a mass of 7.408 kilograms, Sample B has a mass of 7.48 kilograms, and Sample C has a mass of 7.084 kilograms. Which soil sample has the greatest mass? Answer: 7.48 Solution: Write all three masses with the same number of decimal places (to thousandths) for easy comparison: Sample A: 7.408 kg Sample B: 7.480 kg (adding a zero in the thousandths place) Sample C: 7.084 kg Compare the whole number parts (ones place): All are 7, so move to the tenths place.
   Full step-by-step solution

   Step 1: Write all three masses with the same number of decimal places (to thousandths) for easy comparison: Sample A: 7.408 kg Sample B: 7.480 kg (adding a zero in the thousandths place) Sample C: 7.084 kg Step 2: Compare the whole number parts (ones place): All are 7, so move to the tenths place. Step 3: Compare the tenths place: Sample A: 4 tenths Sample B: 4 tenths Sample C: 0 tenths Sample C has fewer tenths, so it is the smallest. Now compare Sample A and Sample B. Step 4: Since Sample A and Sample B are tied in the tenths place, compare the hundredths place: Sample A: 0 hundredths Sample B: 8 hundredths 8 hundredths is greater than 0 hundredths, so Sample B is larger than Sample A. Step 5: Therefore, Sample B (7.48 kg) has the greatest mass. The answer is 7.48.

4. Ava is comparing the weights of three different pumpkins at a fall festival. The orange pumpkin weighs 8.346 kilograms, the striped pumpkin weighs 8.364 kilograms, and the white pumpkin weighs 8.34 kilograms. Which pumpkin is the heaviest? Answer: 8.364 Solution: Write all three weights with the same number of decimal places for easier comparison: Orange pumpkin: 8.346 kg, Striped pumpkin: 8.364 kg, White pumpkin: 8.340 kg.
   Full step-by-step solution

   Step 1: Write all three weights with the same number of decimal places for easier comparison: Orange pumpkin: 8.346 kg, Striped pumpkin: 8.364 kg, White pumpkin: 8.340 kg. Step 2: Compare the whole number parts: All three have 8, so move to the tenths place. Step 3: Compare the tenths place: All three have 3 tenths, so move to the hundredths place. Step 4: Compare the hundredths place: Orange pumpkin has 4 hundredths, Striped pumpkin has 6 hundredths, White pumpkin has 4 hundredths. Since 6 is greater than 4, the striped pumpkin is already heavier than the orange and white pumpkins. Step 5: The striped pumpkin (8.364 kg) is the heaviest. The answer is 8.364.

5. Hana is training for a long-distance running event. She records the distances she runs each day in kilometers. On Monday, she runs 8.305 km. On Tuesday, she runs 8.35 km. On Wednesday, she runs 8.3 km. On Thursday, she runs 8.053 km. Which day did Hana run the greatest distance? Answer: Tuesday Solution: Write all distances with the same number of decimal places (to thousandths) for easy comparison: Monday: 8.305 km Tuesday: 8.350 km (add a zero) Wednesday: 8.300 km (add two zeros) Thursday: 8.053 km Compare the whole number part (ones place).
   Full step-by-step solution

   Step 1: Write all distances with the same number of decimal places (to thousandths) for easy comparison: Monday: 8.305 km Tuesday: 8.350 km (add a zero) Wednesday: 8.300 km (add two zeros) Thursday: 8.053 km Step 2: Compare the whole number part (ones place). All have 8, so move to the tenths place. Step 3: Compare the tenths place: Monday: 3 tenths Tuesday: 3 tenths Wednesday: 3 tenths Thursday: 0 tenths Thursday has the smallest tenths digit, so it is the smallest distance. Step 4: For Monday, Tuesday, and Wednesday, the tenths are all 3, so compare the hundredths place: Monday: 0 hundredths Tuesday: 5 hundredths Wednesday: 0 hundredths Tuesday has the largest hundredths digit (5), so Tuesday's distance is greater than Monday's and Wednesday's. Step 5: Tuesday (8.350 km) is the greatest distance. The answer is Tuesday.

6. 0.75 + 0.3 = ? Answer: 1.05 Solution: Write the problem clearly. 0.75 + 0.3 Align the decimal points to add correctly. 0.75 + 0.30 (We can write 0.3 as 0.30 to make it easier to add) Add the digits in the hundredths place (the farthest right column).
   Full step-by-step solution

   Let's add 0.75 and 0.3 step by step. Step 1: Write the problem clearly. 0.75 + 0.3 Step 2: Align the decimal points to add correctly. Think of it as: 0.75 + 0.30 (We can write 0.3 as 0.30 to make it easier to add) Step 3: Add the digits in the hundredths place (the farthest right column). Hundredths place: 5 + 0 = 5 So, we write ._ _ 5 Step 4: Add the digits in the tenths place. Tenths place: 7 + 3 = 10 Since 10 tenths equals 1 whole, we write down the 0 in the tenths place and carry over the 1 to the ones place. So far we have .0 5 Step 5: Add the digits in the ones place. Ones place: 0 + 0 + 1 (the carried over 1) = 1 So, we write 1 to the left of the decimal. Step 6: Combine the results. We have 1 from the ones place, and .05 from the decimal places. This gives us 1.05. Therefore, 0.75 + 0.3 = 1.05

7. A rectangular prism has 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 in cubic centimeters? 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. Length = 8.5 cm Width = 6.2 cm Height = 4.7 cm Multiply the length and width first.
   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: Multiply the length and width first. 8.5 × 6.2 = ? 8.5 × 6 = 51.0 8.5 × 0.2 = 1.7 Add: 51.0 + 1.7 = 52.7 So, length × width = 52.7 Step 3: Multiply the result by the height. 52.7 × 4.7 = ? First, 52.7 × 4 = 210.8 Then, 52.7 × 0.7 = 36.89 Add: 210.8 + 36.89 = 247.69 Step 4: State the final answer with units. Volume = 247.69 cubic centimeters Thus, the volume of the rectangular prism is 247.69 cm³.