Decimal Operations

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Answer Key & Explanations

Decimal Operations · Grade 5 · Worksheet 2

1. Compare: 7.509 __ 7.519 Answer: < Solution: Compare the ones place: 7 = 7. They are equal. Compare the tenths place: 5 = 5.
   Full step-by-step solution

   Step 1: Compare the ones place: 7 = 7. They are equal. Step 2: Compare the tenths place: 5 = 5. They are equal. Step 3: Compare the hundredths place: 0 < 1. Since 0 is less than 1, 7.509 is less than 7.519. Step 4: The correct symbol is <. The answer is <.

2. A marine biologist is comparing the lengths of two deep-sea creatures. The giant tube worm measures 0.845 meters long, while the vampire squid measures 0.829 meters long. Which creature is longer and by how many meters? Answer: 0.016 Solution: Compare the two decimals: 0.845 and 0.829 Both have 0 in the ones place Both have 8 in the tenths place Compare hundredths place: 4 vs 2, so 0.845 > 0.829 Subtract to find the difference: 0.845 - 0.829 Subtract thousandths: 5 - 9, need to borrow from hundredths 4 hundredths becomes 3 hundredths,…
   Full step-by-step solution

   Step 1: Compare the two decimals: 0.845 and 0.829 Step 2: Both have 0 in the ones place Step 3: Both have 8 in the tenths place Step 4: Compare hundredths place: 4 vs 2, so 0.845 > 0.829 Step 5: Subtract to find the difference: 0.845 - 0.829 Step 6: Subtract thousandths: 5 - 9, need to borrow from hundredths Step 7: 4 hundredths becomes 3 hundredths, 5 thousandths becomes 15 thousandths Step 8: 15 - 9 = 6 thousandths Step 9: 3 - 2 = 1 hundredth Step 10: 8 - 8 = 0 tenths Step 11: 0 - 0 = 0 ones Step 12: The difference is 0.016 meters The answer is 0.016.

3. Hana draws a number line from 0 to 1. She marks point A at 0.375, point B at 0.5, point C at 0.875, and point D at 0.625. If she then draws a point E that is exactly halfway between point A and point C on the number line, what decimal number does point E represent? Answer: 0.625 Solution: Identify the two points. Point A is at 0.375 and point C is at 0.875. To find the halfway point, add the two decimals together: 0.375 + 0.875 = 1.250.
   Full step-by-step solution

   Step 1: Identify the two points. Point A is at 0.375 and point C is at 0.875. Step 2: To find the halfway point, add the two decimals together: 0.375 + 0.875 = 1.250. Step 3: Divide the sum by 2: 1.250 / 2 = 0.625. Step 4: Check: The distance from 0.375 to 0.625 is 0.250, and the distance from 0.625 to 0.875 is also 0.250. So 0.625 is exactly halfway. The answer is 0.625.

4. A rectangular garden is drawn on a coordinate plane with corners at (2.5, 1.5), (8.5, 1.5), (8.5, 4.5), and (2.5, 4.5). What is the area of this garden in square units? Answer: 18 Solution: Identify the length by finding the difference in x-coordinates between two points on the same horizontal line. Points (2.5, 1.5) and (8.5, 1.5) have the same y-coordinate.
   Full step-by-step solution

   Step 1: Identify the length by finding the difference in x-coordinates between two points on the same horizontal line. Points (2.5, 1.5) and (8.5, 1.5) have the same y-coordinate. Length = 8.5 - 2.5 = 6 units Step 2: Identify the width by finding the difference in y-coordinates between two points on the same vertical line. Points (2.5, 1.5) and (2.5, 4.5) have the same x-coordinate. Width = 4.5 - 1.5 = 3 units Step 3: Calculate the area using the formula: Area = length × width Area = 6 × 3 = 18 square units The area of the garden is 18 square units.

5. A rectangular prism has a length of 12.5 cm, a width of 8.4 cm, and a height of 6.3 cm. What is the volume of this prism in cubic centimeters? Answer: 661.5 Solution: Write the volume formula for a rectangular prism: Volume = length × width × height Substitute the given measurements: Volume = 12.5 × 8.4 × 6.3 First multiply 12.5 × 8.4 = 105 Then multiply 105 × 6.3 = 661.5 The volume is 661.5 cubic centimeters
   Full step-by-step solution

   Step 1: Write the volume formula for a rectangular prism: Volume = length × width × height Step 2: Substitute the given measurements: Volume = 12.5 × 8.4 × 6.3 Step 3: First multiply 12.5 × 8.4 = 105 Step 4: Then multiply 105 × 6.3 = 661.5 Step 5: The volume is 661.5 cubic centimeters

6. Emma is measuring the lengths of three different pieces of string for a craft project. The red string is 7.389 centimeters long, the blue string is 7.398 centimeters long, and the green string is 7.38 centimeters long. Which piece of string is the longest? Answer: 7.398 Solution: Write all three lengths with the same number of decimal places: Red = 7.389 cm, Blue = 7.398 cm, Green = 7.380 cm. Compare the ones place: All have 7, so move to the tenths place.
   Full step-by-step solution

   Step 1: Write all three lengths with the same number of decimal places: Red = 7.389 cm, Blue = 7.398 cm, Green = 7.380 cm. Step 2: Compare the ones place: All have 7, so move to the tenths place. Step 3: Compare the tenths place: All have 3, so move to the hundredths place. Step 4: Compare the hundredths place: Red has 8, Blue has 9, Green has 8. Blue has the largest hundredths digit (9), so it is already the longest. Step 5: Even though we can check the thousandths place for Red and Green, Blue's 9 hundredths is greater than 8 hundredths, so Blue is longest. The answer is 7.398.

7. 2.75 + 1.3 = ? Answer: 4.05 Solution: Write the numbers vertically, aligning the decimal points. 2.75 + 1.30 Add the numbers in the hundredths place: 5 + 0 = 5. Write 5 in the hundredths place.
   Full step-by-step solution

   Step 1: Write the numbers vertically, aligning the decimal points. 2.75 + 1.30 ------- Step 2: Add the numbers in the hundredths place: 5 + 0 = 5. Write 5 in the hundredths place. Step 3: Add the numbers in the tenths place: 7 + 3 = 10. Write 0 in the tenths place and carry over 1 to the ones place. Step 4: Add the numbers in the ones place: 2 + 1 + 1 (carried over) = 4. Write 4 in the ones place. Step 5: Bring down the decimal point. The final answer is 4.05.