Round Decimals

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Answer Key & Explanations

Round Decimals · Grade 5 · Worksheet 2

1. Mere is measuring the length of a hiking trail for a school project. The trail marker shows the distance is 6.284 kilometers. She needs to record this distance rounded to the nearest tenth of a kilometer in her report. What distance should Mere write down? Answer: 6.3 Solution: Identify the place values in 6.284. The tenths place is the first digit after the decimal point, which is 2. The hundredths place is the second digit after the decimal, which is 8.
   Full step-by-step solution

   Step 1: Identify the place values in 6.284. The tenths place is the first digit after the decimal point, which is 2. The hundredths place is the second digit after the decimal, which is 8. The thousandths place is the third digit, which is 4. Step 2: We are rounding to the nearest tenth, so we look at the digit in the hundredths place, which is 8. Step 3: Since 8 is greater than or equal to 5, we round the tenths digit up from 2 to 3. Step 4: All digits to the right of the tenths place become zero, so we get 6.300, which simplifies to 6.3. The answer is 6.3.

2. Round 7.836 to the nearest hundredth. Answer: 7.84 Solution: To round 7.836 to the nearest hundredth, follow these steps: Identify the hundredths place.
   Full step-by-step solution

   To round 7.836 to the nearest hundredth, follow these steps: Step 1: Identify the hundredths place. In the number 7.836, the digits after the decimal point represent: - 8 is the tenths place - 3 is the hundredths place - 6 is the thousandths place So, the digit in the hundredths place is 3. Step 2: Look at the digit immediately to the right of the hundredths place. This is the thousandths place, which is 6. Step 3: Apply the rounding rule. If the digit in the thousandths place is 5 or greater (which it is, since 6 >= 5), we round the hundredths digit up by 1. Step 4: Perform the rounding. The hundredths digit is 3. Rounding it up by 1 changes it to 4. The digits to the left of the hundredths place (the 7 and the 8) remain the same. The digits after the hundredths place are dropped. Step 5: Write the final rounded number. Combining these, we get 7.84. Therefore, 7.836 rounded to the nearest hundredth is 7.84.

3. Liam is measuring the length of a new bookshelf for his classroom. The tape measure shows the shelf is 2.875 meters long. What is the length of the bookshelf rounded to the nearest tenth of a meter? Answer: 2.9 Solution: Length = 2.875 meters We need to round to the nearest tenth of a meter. Identify the digit in the tenths place and the digit in the hundredths place.
   Full step-by-step solution

   Let's go step-by-step. We are given: Length = 2.875 meters We need to round to the nearest tenth of a meter. --- **Step 1: Identify the digit in the tenths place and the digit in the hundredths place.** Write the number: 2.875 - The tenths place is the first digit after the decimal point: 8 - The hundredths place is the second digit after the decimal point: 7 - The thousandths place is the third digit after the decimal point: 5 So: 2 . 8 7 5 ↑ ↑ tenths hundredths --- **Step 2: Rounding rule for nearest tenth** Look at the hundredths digit (7) to decide whether to round the tenths digit up or keep it the same. Rule: - If hundredths digit is 5 or greater → round the tenths digit up by 1. - If hundredths digit is 4 or less → keep the tenths digit the same. Here, hundredths digit = 7, which is greater than 5, so we round the tenths digit (8) up by 1. --- **Step 3: Perform the rounding** Tenths digit 8 + 1 = 9 Replace digits after the tenths place with zeros (in decimal sense, they disappear when rounding). So 2.875 → 2.9 --- **Step 4: Check the result** 2.9 means 2.900, which is indeed 2.875 rounded to the nearest tenth because 2.875 is closer to 2.9 than to 2.8. --- **Final Answer:** 2.9

4. Round 6.3847 to the nearest hundredth. Answer: 6.38 Solution: The number is 6.3847. The hundredths place is the second digit after the decimal point. In 6.3847, the digit in the hundredths place is 8.
   Full step-by-step solution

   Step 1: The number is 6.3847. Step 2: The hundredths place is the second digit after the decimal point. In 6.3847, the digit in the hundredths place is 8. Step 3: Look at the digit to the right of the hundredths place, which is the thousandths place. The digit in the thousandths place is 4. Step 4: Since 4 is less than 5, we do not round up. The digit in the hundredths place (8) stays the same. Step 5: All digits to the right of the hundredths place are dropped. Therefore, 6.3847 rounded to the nearest hundredth is 6.38.

5. Maria is tracking the growth of her sunflower plant for a science project. After 3 weeks, her plant has grown to 4.637 meters tall. She needs to record the height rounded to the nearest hundredth of a meter in her science journal. What height should Maria write down? Answer: 4.64 Solution: Identify the hundredths place in 4.637. The hundredths place is the second digit after the decimal point, which is 3.
   Full step-by-step solution

   Step 1: Identify the hundredths place in 4.637. The hundredths place is the second digit after the decimal point, which is 3. Step 2: Look at the digit immediately 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 place up from 3 to 4. Step 4: The digits before the hundredths place remain the same: 4.6 Step 5: Combine to get the rounded number: 4.64 The answer is 4.64.

6. Isabella is helping her dad build a new birdhouse. They measured a wooden plank and it is 3.627 meters long. The instructions say they need the length rounded to the nearest hundredth of a meter to fit the next piece correctly. What length should Isabella tell her dad to cut the plank to? Answer: 3.63 Solution: Identify the hundredths place in 3.627. The hundredths place is the second digit after the decimal point, which is 2. Look at the digit immediately to the right of the hundredths place.
   Full step-by-step solution

   Step 1: Identify the hundredths place in 3.627. The hundredths place is the second digit after the decimal point, which is 2. Step 2: Look at the digit immediately to the right of the hundredths place. That is the thousandths place, which is 7. Step 3: The rule for rounding: if the digit to the right is 5 or greater, round up the hundredths digit by 1. Since 7 is greater than 5, we round the 2 up to 3. Step 4: All digits to the right of the hundredths place become zero, so we have 3.630. We can drop the trailing zero to write 3.63. The answer is 3.63.

7. Matiu is drawing a rectangular garden on a coordinate grid. The four corners of the garden are at (15.2, 23.7), (15.2, 8.3), (42.6, 8.3), and (42.6, 23.7). What is the perimeter of the garden in units? Round your answer to the nearest tenth. Answer: 85.6 Solution: Find the length (horizontal distance). The x-coordinates are 15.2 and 42.6. Length = 42.6 - 15.2 = 27.4 units.
   Full step-by-step solution

   Step 1: Find the length (horizontal distance). The x-coordinates are 15.2 and 42.6. Length = 42.6 - 15.2 = 27.4 units. Step 2: Find the width (vertical distance). The y-coordinates are 23.7 and 8.3. Width = 23.7 - 8.3 = 15.4 units. Step 3: Use the perimeter formula for a rectangle: P = 2 × (length + width) = 2 × (27.4 + 15.4) = 2 × 42.8 = 85.6 units. Step 4: The answer is already to the nearest tenth: 85.6. The perimeter is 85.6 units.

8. Liam is measuring the length of a new bookshelf for his classroom. The tape measure shows the shelf is 2.375 meters long. His teacher asks him to report this measurement rounded to the nearest tenth of a meter. What length should Liam report? Answer: 2.4 Solution: We start with the measurement 2.375 meters. We need to round this to the nearest tenth of a meter. The tenths place is the first digit after the decimal point.
   Full step-by-step solution

   Step 1: Understand the problem. We start with the measurement 2.375 meters. We need to round this to the nearest tenth of a meter. The tenths place is the first digit after the decimal point. Step 2: Identify the rounding digit and the digit that follows it. Write the number: 2.375 - The tenths place is the digit 3 (2.3 means 2 and 3 tenths). - The digit immediately after the tenths place (the hundredths place) is 7. Step 3: Apply rounding rules. If the hundredths digit is 5 or greater, we round the tenths digit up by 1. If the hundredths digit is 4 or less, we keep the tenths digit the same. Here, the hundredths digit is 7, which is 5 or greater. Step 4: Round up the tenths digit. Tenths digit = 3. Round up 3 to 4. Drop all digits after the tenths place. Step 5: Write the rounded number. 2.375 rounded to the nearest tenth becomes 2.4. Final answer: 2.4