Worksheet 1Worksheet 2Worksheet 3

The download includes this worksheet followed by the answer key with explanations. In the print dialog choose “Save as PDF” to download.

lessonbunny.com
Name: ______________________________ Date: ______________

Decimal Operations

Grade 5 · Decimals · Worksheet 1

  1. Compare: 8.409 __ 8.49 Answer: ______________
  2. 3.75 + 2.125 = ? Answer: ______________
  3. 0.85 + 1.47 = ? Answer: ______________
  4. Noah is comparing the weights of three different pumpkins he grew in his garden. The Atlantic Giant pumpkin weighs 7.816 kilograms, the Big Max pumpkin weighs 7.861 kilograms, and the Jarrahdale pumpkin weighs 7.68 kilograms. Which pumpkin is the heaviest? Answer: ______________
  5. Emma is comparing the lengths of three different hiking trails for her outdoor club. The Pine Trail is 2.345 kilometers long, the Maple Trail is 2.354 kilometers long, and the Oak Trail is 2.35 kilometers long. Which trail is the longest? Answer: ______________
  6. Emma draws a number line from 0 to 1 and marks three points: A at 0.375, B at 0.5, and C at 0.875. Then she draws a rectangle on a coordinate grid where the bottom-left corner is at (0.375, 0.5) and the top-right corner is at (0.875, 0.75). What is the area of the rectangle in square units? Answer: ______________
  7. Noah is comparing the distances of three different running routes in his neighborhood. The Oak Street Loop is 7.893 kilometers long, the Pine Avenue Circuit is 7.839 kilometers long, and the Elm Park Path is 7.9 kilometers long. Which running route is the longest? Answer: ______________
  8. Kaia is training for a long-distance cycling event. She recorded the distances of three different training routes she rode last week. The River Loop is 9.407 kilometers, the Hill Climb is 9.47 kilometers, and the Forest Trail is 9.074 kilometers. Which training route is the longest? Answer: ______________
lessonbunny.com

Answer Key & Explanations

Decimal Operations · Grade 5 · Worksheet 1

  1. Compare: 8.409 __ 8.49 Answer: < Solution: Write the numbers with the same number of decimal places: 8.409 and 8.490. Compare the digits from left to right.
    Full step-by-step solution

    Step 1: Write the numbers with the same number of decimal places: 8.409 and 8.490. Step 2: Compare the digits from left to right. - Ones place: 8 = 8 (same) - Tenths place: 4 = 4 (same) - Hundredths place: 0 < 9 Step 3: Since 0 is less than 9 in the hundredths place, 8.409 is less than 8.49. The answer is <.

  2. 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.

  3. 0.85 + 1.47 = ? Answer: 2.32 Solution: 0.85 + 1.47 Add the hundredths place: 5 + 7 = 12. Write down 2 in the hundredths place and carry over 1 to the tenths place. Add the tenths place: 8 + 4 + 1 (carried over) = 13.
    Full step-by-step solution

    Step 1: Write the numbers with decimal points aligned: 0.85 + 1.47 Step 2: Add the hundredths place: 5 + 7 = 12. Write down 2 in the hundredths place and carry over 1 to the tenths place. Step 3: Add the tenths place: 8 + 4 + 1 (carried over) = 13. Write down 3 in the tenths place and carry over 1 to the ones place. Step 4: Add the ones place: 0 + 1 + 1 (carried over) = 2. Write down 2 in the ones place. Step 5: Place the decimal point in the answer directly below the decimal points in the numbers being added. The final answer is 2.32.

  4. Noah is comparing the weights of three different pumpkins he grew in his garden. The Atlantic Giant pumpkin weighs 7.816 kilograms, the Big Max pumpkin weighs 7.861 kilograms, and the Jarrahdale pumpkin weighs 7.68 kilograms. Which pumpkin is the heaviest? Answer: 7.861 Solution: Write all three weights with the same number of decimal places (thousandths). Atlantic Giant = 7.816, Big Max = 7.861, Jarrahdale = 7.680. Step 2: Compare the whole number (ones) place.
    Full step-by-step solution

    Step 1: Write all three weights with the same number of decimal places (thousandths). Atlantic Giant = 7.816, Big Max = 7.861, Jarrahdale = 7.680. Step 2: Compare the whole number (ones) place. All have 7, so move to the tenths place. Step 3: Compare the tenths place. Atlantic Giant has 8 tenths, Big Max has 8 tenths, Jarrahdale has 6 tenths. Since 6 is less than 8, Jarrahdale is the lightest. Step 4: Now compare Atlantic Giant and Big Max. They both have 8 tenths, so look at the hundredths place. Atlantic Giant has 1 hundredth, Big Max has 6 hundredths. Since 6 is greater than 1, Big Max is heavier. Therefore, the Big Max pumpkin at 7.861 kilograms is the heaviest. The answer is 7.861.

  5. Emma is comparing the lengths of three different hiking trails for her outdoor club. The Pine Trail is 2.345 kilometers long, the Maple Trail is 2.354 kilometers long, and the Oak Trail is 2.35 kilometers long. Which trail is the longest? Answer: 2.354 Solution: Write all three trail lengths with the same number of decimal places: Pine Trail: 2.345 km Maple Trail: 2.354 km Oak Trail: 2.350 km (adding a zero to make it thousandths) Compare the whole number parts - all are 2, so move to tenths place.
    Full step-by-step solution

    Step 1: Write all three trail lengths with the same number of decimal places: Pine Trail: 2.345 km Maple Trail: 2.354 km Oak Trail: 2.350 km (adding a zero to make it thousandths) Step 2: Compare the whole number parts - all are 2, so move to tenths place. All have 3 in the tenths place, so move to hundredths place. Step 3: Compare hundredths place: Pine Trail: 4 hundredths Maple Trail: 5 hundredths Oak Trail: 5 hundredths Maple Trail and Oak Trail both have 5 hundredths, while Pine Trail has only 4. Step 4: Since Maple Trail and Oak Trail are tied so far, compare thousandths place: Maple Trail: 4 thousandths Oak Trail: 0 thousandths Step 5: Since 4 thousandths is greater than 0 thousandths, Maple Trail (2.354) is the longest. The answer is 2.354.

  6. Emma draws a number line from 0 to 1 and marks three points: A at 0.375, B at 0.5, and C at 0.875. Then she draws a rectangle on a coordinate grid where the bottom-left corner is at (0.375, 0.5) and the top-right corner is at (0.875, 0.75). What is the area of the rectangle in square units? Answer: 0.125 Solution: Find the length by subtracting the x-coordinates: 0.875 - 0.375 = 0.500 Find the width by subtracting the y-coordinates: 0.75 - 0.5 = 0.25 Calculate the area using the formula: Area = length x width Area = 0.500 x 0.25 Multiply: 0.500 x 0.25 = 0.125 The area of the rectangle is 0.125 square units.
    Full step-by-step solution

    Step 1: Find the length by subtracting the x-coordinates: 0.875 - 0.375 = 0.500 Step 2: Find the width by subtracting the y-coordinates: 0.75 - 0.5 = 0.25 Step 3: Calculate the area using the formula: Area = length x width Area = 0.500 x 0.25 Step 4: Multiply: 0.500 x 0.25 = 0.125 The area of the rectangle is 0.125 square units.

  7. Noah is comparing the distances of three different running routes in his neighborhood. The Oak Street Loop is 7.893 kilometers long, the Pine Avenue Circuit is 7.839 kilometers long, and the Elm Park Path is 7.9 kilometers long. Which running route is the longest? Answer: 7.9 Solution: Write all three distances with the same number of decimal places for easy comparison: Oak Street Loop: 7.893 km Pine Avenue Circuit: 7.839 km Elm Park Path: 7.900 km Compare the whole number parts.
    Full step-by-step solution

    Step 1: Write all three distances with the same number of decimal places for easy comparison: Oak Street Loop: 7.893 km Pine Avenue Circuit: 7.839 km Elm Park Path: 7.900 km Step 2: Compare the whole number parts. All have 7, so move to the tenths place. Step 3: Compare the tenths place: Oak Street Loop: 8 tenths Pine Avenue Circuit: 8 tenths Elm Park Path: 9 tenths Since 9 tenths is greater than 8 tenths, the Elm Park Path is already the longest. Step 4: Therefore, Elm Park Path (7.9 km) is the longest running route. The answer is 7.9.

  8. Kaia is training for a long-distance cycling event. She recorded the distances of three different training routes she rode last week. The River Loop is 9.407 kilometers, the Hill Climb is 9.47 kilometers, and the Forest Trail is 9.074 kilometers. Which training route is the longest? Answer: 9.47 Solution: Write all three distances with the same number of decimal places for easy comparison: - River Loop: 9.407 - Hill Climb: 9.470 (add a zero to thousandths) - Forest Trail: 9.074 Compare the whole number parts: All have 9, so move to the tenths place.
    Full step-by-step solution

    Step 1: Write all three distances with the same number of decimal places for easy comparison: - River Loop: 9.407 - Hill Climb: 9.470 (add a zero to thousandths) - Forest Trail: 9.074 Step 2: Compare the whole number parts: All have 9, so move to the tenths place. Step 3: Compare the tenths place: - River Loop: 4 tenths - Hill Climb: 4 tenths - Forest Trail: 0 tenths Forest Trail has fewer tenths, so it is the shortest. Now compare River Loop and Hill Climb. Step 4: Compare the hundredths place: - River Loop: 0 hundredths - Hill Climb: 7 hundredths Since 7 hundredths is greater than 0 hundredths, Hill Climb is longer than River Loop. Step 5: The longest route is the Hill Climb at 9.47 kilometers. The answer is 9.47.