Round Decimals

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Answer Key & Explanations

Round Decimals · Grade 5 · Worksheet 3

1. Round 6.495 to the nearest hundredth. Answer: 6.50 Solution: Identify the hundredths place: 6.49(5). The hundredths digit is 9. Look at the digit to the right (thousandths place), which is 5.
   Full step-by-step solution

   Step 1: Identify the hundredths place: 6.49(5). The hundredths digit is 9. Step 2: Look at the digit to the right (thousandths place), which is 5. Step 3: Since the thousandths digit is 5 or greater, we round the hundredths digit up. Step 4: Rounding 9 up makes it 10, so we write 0 in the hundredths place and carry 1 to the tenths place. Step 5: The tenths digit is 4, plus the carried 1 becomes 5. Step 6: The final rounded number is 6.50. The answer is 6.50.

2. A rectangular prism-shaped shipping box has a length of 14.6 cm, a width of 9.3 cm, and a height of 12.8 cm. What is the volume of this box in cubic centimeters? Answer: 1737.984 Solution: Write the volume formula for a rectangular prism: Volume = length × width × height Substitute the given values: Volume = 14.6 × 9.3 × 12.8 Multiply the first two numbers: 14.6 × 9.3 = 135.78 Multiply the result by the height: 135.78 × 12.8 = 1737.984 The volume is 1737.984 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 values: Volume = 14.6 × 9.3 × 12.8 Step 3: Multiply the first two numbers: 14.6 × 9.3 = 135.78 Step 4: Multiply the result by the height: 135.78 × 12.8 = 1737.984 Step 5: The volume is 1737.984 cubic centimeters.

3. Liam is measuring the length of his new bookshelf for his bedroom. His tape measure shows the shelf is 2.375 meters long. He needs to report this measurement to the nearest tenth of a meter for a furniture catalog. What is the length of the bookshelf rounded to the nearest tenth? Answer: 2.4 Solution: We start with the measurement: 2.375 meters. We need to round it to the nearest tenth of a meter. Identify the digit in the tenths place and the digit immediately after it.
   Full step-by-step solution

   Let's go step-by-step. We start with the measurement: 2.375 meters. We need to round it to the nearest tenth of a meter. **Step 1: Identify the digit in the tenths place and the digit immediately after it.** 2.375 - The tenths place is the first digit after the decimal point: 3 - The hundredths place is the next digit: 7 **Step 2: Look at the hundredths digit to decide whether to round up or keep the same.** Rule: If the hundredths digit is 5 or greater, round the tenths digit up by 1. If the hundredths digit is 4 or less, keep the tenths digit the same. Here, the hundredths digit is 7, which is greater than or equal to 5. **Step 3: Round the tenths digit up.** Tenths digit = 3 → increase by 1 → becomes 4. **Step 4: Drop all digits after the tenths place.** Before rounding: 2.375 After rounding to nearest tenth: 2.4 **Step 5: Final check** 2.375 is closer to 2.4 than to 2.3, so 2.4 is correct. **Final answer:** 2.4

4. Liam is measuring the length of a new bookshelf for his classroom. The shelf measures 2.375 meters long. He needs to report this measurement to the nearest tenth of a meter for the school inventory list. What is the length of the bookshelf rounded to the nearest tenth? Answer: 2.4 Solution: Identify the digit in the tenths place and the digit in the hundredths place. The number is 2.375. - The tenths place is the first digit after the decimal point: 3.
   Full step-by-step solution

   Step 1: Identify the digit in the tenths place and the digit in the hundredths place. The number is 2.375. - The tenths place is the first digit after the decimal point: 3. - The hundredths place is the second digit after the decimal point: 7. Step 2: Look at the hundredths digit to decide whether to round the tenths digit up or keep it the same. The rounding rule is: - If the hundredths digit is 5 or greater, round the tenths digit up by 1. - If the hundredths digit is 4 or less, keep the tenths digit the same. Step 3: Apply the rule. Here, the hundredths digit is 7, which is 5 or greater, so we round the tenths digit (3) up by 1. 3 + 1 = 4 in the tenths place. Step 4: Replace digits after the tenths place with zeros (but since we are rounding to the nearest tenth, we drop them). So, 2.375 becomes 2.4 after rounding. Final Answer: 2.4

5. Round 3.789 to the nearest hundredth. Answer: 3.79 Solution: Identify the hundredths place. In the number 3.789, the digits after the decimal point represent: - 7 (tenths place) - 8 (hundredths place) - 9 (thousandths place) So, 3.789 means 3 and 7 tenths, 8 hundredths, and 9 thousandths.
   Full step-by-step solution

   Step 1: Identify the hundredths place. In the number 3.789, the digits after the decimal point represent: - 7 (tenths place) - 8 (hundredths place) - 9 (thousandths place) So, 3.789 means 3 and 7 tenths, 8 hundredths, and 9 thousandths. Step 2: Look at the thousandths digit to decide whether to round the hundredths digit up or keep it the same. The thousandths digit is 9. Rounding rule: If the thousandths digit is 5 or greater, round the hundredths digit up by 1. If it is 4 or less, keep the hundredths digit the same. Step 3: Apply the rounding rule. Since the thousandths digit is 9 (which is 5 or greater), we round the hundredths digit (8) up by 1. 8 + 1 = 9. Step 4: Replace the thousandths digit with zero (or simply drop it since we are rounding to hundredths). Original: 3.789 After rounding hundredths place up: 3.79 Step 5: Final answer. 3.789 rounded to the nearest hundredth is 3.79.

6. Maria is tracking the growth of her sunflower plant for a science project. After 2 weeks, it has grown to 4.837 meters tall. She needs to record the height rounded to the nearest hundredth of a meter in her project journal. What height should Maria write down? Answer: 4.84 Solution: Identify the hundredths place in 4.837. The digits are: 4 (ones), 8 (tenths), 3 (hundredths), 7 (thousandths). Look at the digit to the right of the hundredths place, which is 7 in the thousandths place.
   Full step-by-step solution

   Step 1: Identify the hundredths place in 4.837. The digits are: 4 (ones), 8 (tenths), 3 (hundredths), 7 (thousandths). Step 2: Look at the digit to the right of the hundredths place, which is 7 in the thousandths place. Step 3: Since 7 is greater than or equal to 5, we round the hundredths digit (3) up by 1. Step 4: 3 becomes 4, so 4.837 rounded to the nearest hundredth is 4.84. The answer is 4.84.

7. round(3.785, 2) = ? Answer: 3.79 Solution: Step 1: Identify the digit in the hundredths place (second decimal place): 8 Step 2: Look at the digit in the thousandths place (third decimal place): 5 Step 3: Since the thousandths digit is 5 or greater, we round up the hundredths digit from 8 to 9 Step 4: The rounded number becomes 3.79 Step…
   Full step-by-step solution

   Step 1: Identify the digit in the hundredths place (second decimal place): 8 Step 2: Look at the digit in the thousandths place (third decimal place): 5 Step 3: Since the thousandths digit is 5 or greater, we round up the hundredths digit from 8 to 9 Step 4: The rounded number becomes 3.79 Step 5: Verify: 3.785 rounded to two decimal places is 3.79