Round Decimals

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Answer Key & Explanations

Round Decimals · Grade 5 · Worksheet 2

1. Liam is measuring the length of his new bookshelf for his bedroom. The tape measure shows the shelf is 3.456 meters long. His dad asks him to report the length rounded to the nearest hundredth of a meter. What length should Liam tell his dad? Answer: 3.46 Solution: Identify the given measurement and the rounding requirement. The shelf length is 3.456 meters. We need to round it to the nearest hundredth of a meter.
   Full step-by-step solution

   Step 1: Identify the given measurement and the rounding requirement. The shelf length is 3.456 meters. We need to round it to the nearest hundredth of a meter. The hundredth place is the second digit after the decimal point. Step 2: Write the number with place values labeled. 3.456 means: 3 (ones) . 4 (tenths) 5 (hundredths) 6 (thousandths) Step 3: Since we are rounding to the nearest hundredth, we look at the thousandths digit to decide whether to round the hundredths digit up or keep it the same. The thousandths digit is 6. Step 4: Apply the rounding rule: If the thousandths digit is 5 or greater, we round the hundredths digit up by 1. If the thousandths digit is 4 or less, we leave the hundredths digit unchanged. Here, the thousandths digit is 6, which is 5 or greater, so we round the hundredths digit (5) up by 1. Step 5: Perform the rounding: Hundredths digit = 5, rounding up makes it 6. Digits before the hundredths place remain the same: 3.4 So 3.45 becomes 3.46 after rounding up. Step 6: Write the final rounded number. 3.456 rounded to the nearest hundredth is 3.46. Answer: 3.46

2. Liam is measuring the length of a new bookshelf for his classroom. The tape measure shows 2.385 meters. His teacher asks him to round this measurement to the nearest hundredth of a meter for their records. What measurement should Liam write down? Answer: 2.39 Solution: The measurement is 2.385 meters.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Understand the number and place values** The measurement is **2.385 meters**. Let's label each digit after the decimal point by its place value: - 2 . 3 8 5 - The digits after the decimal point are: 3 → tenths (1/10) 8 → hundredths (1/100) 5 → thousandths (1/1000) We are rounding to the **nearest hundredth**, so we focus on the hundredths place (8) and the digit immediately after it (5). --- **Step 2: Identify the rounding digit and the test digit** - Rounding digit (hundredths place) = 8 - Test digit (thousandths place) = 5 --- **Step 3: Apply rounding rules** Rule: If the test digit is **5 or more**, round the rounding digit up by 1. If the test digit is **less than 5**, keep the rounding digit the same. Here, test digit = 5 → so we round the hundredths digit (8) up by 1. --- **Step 4: Perform the rounding** 8 + 1 = 9 in the hundredths place. Digits before the hundredths place remain the same: 2.38... becomes 2.39 after rounding. --- **Step 5: Write the final rounded number** The thousandths place and beyond are dropped after rounding. So: 2.385 → 2.39 --- **Final Answer:** 2.39

3. Mere is measuring the weight of her pumpkin for the school's annual pumpkin-growing contest. Her pumpkin weighs 5.628 kilograms. The contest rules require all weights to be reported rounded to the nearest tenth of a kilogram. What weight should Mere report for her pumpkin? Answer: 5.6 Solution: Identify the tenths place in 5.628. The tenths place is the first digit after the decimal point, which is 6. Look at the digit to the right of the tenths place.
   Full step-by-step solution

   Step 1: Identify the tenths place in 5.628. The tenths place is the first digit after the decimal point, which is 6. Step 2: Look at the digit to the right of the tenths place. That is the hundredths place, which is 2. Step 3: Since 2 is less than 5, we do not round up the tenths digit. The tenths digit stays as 6. Step 4: All digits to the right of the tenths place become zero, so we get 5.600, which simplifies to 5.6. The answer is 5.6.

4. 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.

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 3 weeks, her plant has grown to 4.762 centimeters tall. She needs to record this measurement rounded to the nearest hundredth of a centimeter in her project journal. What height should Maria write down? Answer: 4.76 Solution: Identify the hundredths place in 4.762. The hundredths place is the second digit after the decimal point, which is 6. Look at the digit immediately to the right of the hundredths place, which is the thousandths place.
   Full step-by-step solution

   Step 1: Identify the hundredths place in 4.762. The hundredths place is the second digit after the decimal point, which is 6. Step 2: Look at the digit immediately to the right of the hundredths place, which is the thousandths place. In 4.762, the thousandths digit is 2. Step 3: Since 2 is less than 5, we keep the hundredths digit the same and drop all digits to the right. Step 4: 4.762 rounded to the nearest hundredth is 4.76. The answer is 4.76.