Decimal Operations

lessonbunny.com

Answer Key & Explanations

Decimal Operations · Grade 5 · Worksheet 1

1. A rectangular prism-shaped fish tank has a length of 12.5 cm, a width of 8.4 cm, and a height of 10.2 cm. What is the volume of this fish tank in cubic centimeters? Answer: 1071 Solution: Identify the formula for the volume of a rectangular prism: Volume = length × width × height. Substitute the given measurements into the formula: Volume = 12.5 cm × 8.4 cm × 10.2 cm.
   Full step-by-step solution

   Step 1: Identify the formula for the volume of a rectangular prism: Volume = length × width × height. Step 2: Substitute the given measurements into the formula: Volume = 12.5 cm × 8.4 cm × 10.2 cm. Step 3: First, multiply the length and width: 12.5 × 8.4 = 105. Step 4: Now multiply that result by the height: 105 × 10.2 = 1071. Step 5: The volume is 1071 cubic centimeters.

2. Emma is comparing the lengths of three different hiking trails for her outdoor club. The Pine Trail is 2.345 kilometers long, the Oak Trail is 2.354 kilometers long, and the Maple 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 by adding zeros where needed: Pine Trail: 2.345 km Oak Trail: 2.354 km Maple Trail: 2.350 km All three have 2 as the whole number, so we need to compare the decimal parts.
   Full step-by-step solution

   Step 1: Write all three trail lengths with the same number of decimal places by adding zeros where needed: Pine Trail: 2.345 km Oak Trail: 2.354 km Maple Trail: 2.350 km Step 2: Compare the whole number parts (left of decimal): All three have 2 as the whole number, so we need to compare the decimal parts. Step 3: Compare the tenths place (first digit after decimal): All three have 3 in the tenths place, so we need to compare the hundredths place. Step 4: Compare the hundredths place (second digit after decimal): Pine Trail: 4 Oak Trail: 5 Maple Trail: 5 Since 5 is greater than 4, both Oak Trail and Maple Trail are longer than Pine Trail. Step 5: Compare the thousandths place (third digit after decimal) for Oak Trail and Maple Trail: Oak Trail: 4 Maple Trail: 0 Since 4 is greater than 0, Oak Trail is longer than Maple Trail. Step 6: Therefore, the Oak Trail (2.354 km) is the longest. The answer is 2.354.

3. Noah is training for a long-distance race. On Monday, he ran 3.581 kilometers. On Wednesday, he ran 3.561 kilometers. On Friday, he ran 3.6 kilometers. Which day did Noah run the farthest distance? Answer: Monday Solution: Write all distances with the same number of decimal places (to thousandths): Monday: 3.581 km Wednesday: 3.561 km Friday: 3.600 km All three have 3 in the ones place, so they are equal so far.
   Full step-by-step solution

   Step 1: Write all distances with the same number of decimal places (to thousandths): Monday: 3.581 km Wednesday: 3.561 km Friday: 3.600 km Step 2: Compare the whole number part (ones place): All three have 3 in the ones place, so they are equal so far. Step 3: Compare the tenths place: Monday: 5 tenths Wednesday: 5 tenths Friday: 6 tenths Friday has 6 tenths, which is greater than 5 tenths, so Friday is longer than Monday and Wednesday. Step 4: But we must check if any distance is greater than Friday. Compare Monday and Wednesday to Friday: Friday (3.600) has 6 tenths, while Monday (3.581) has 5 tenths and Wednesday (3.561) has 5 tenths. So Friday is already the greatest. Step 5: The farthest distance is 3.600 km (Friday). The answer is Friday.

4. 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

5. Aroha is comparing the weights of three different fruits at the market. A pumpkin weighs 3.507 kilograms, a watermelon weighs 3.57 kilograms, and a cantaloupe weighs 3.075 kilograms. Which fruit is the heaviest? Answer: 3.57 Solution: Write all three weights with the same number of decimal places for easy comparison: Pumpkin: 3.507 kg Watermelon: 3.570 kg (add a zero to the thousandths place) Cantaloupe: 3.075 kg Compare the whole number parts.
   Full step-by-step solution

   Step 1: Write all three weights with the same number of decimal places for easy comparison: Pumpkin: 3.507 kg Watermelon: 3.570 kg (add a zero to the thousandths place) Cantaloupe: 3.075 kg Step 2: Compare the whole number parts. All have 3, so move to the tenths place. Step 3: Compare the tenths place: Pumpkin: 5 tenths Watermelon: 5 tenths Cantaloupe: 0 tenths Cantaloupe is smaller, so it is not the heaviest. Step 4: Compare the hundredths place for Pumpkin and Watermelon: Pumpkin: 0 hundredths Watermelon: 7 hundredths 7 hundredths is greater than 0 hundredths. Step 5: Since Watermelon has 7 hundredths and Pumpkin has 0 hundredths, the watermelon is heavier. The heaviest fruit is the watermelon, weighing 3.57 kilograms.

6. 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 <.