Round Decimals

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Answer Key & Explanations

Round Decimals · Grade 5 · Worksheet 3

1. A rectangular prism-shaped fish tank has a length of 12.5 cm, a width of 8.2 cm, and a height of 15.7 cm. What is the volume of the fish tank in cubic centimeters? Answer: 1609.25 Solution: To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Write down the given dimensions. Length = 12.5 cm Width = 8.2 cm Height = 15.7 cm Multiply the length and width first.
   Full step-by-step solution

   To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Step 1: Write down the given dimensions. Length = 12.5 cm Width = 8.2 cm Height = 15.7 cm Step 2: Multiply the length and width first. 12.5 × 8.2 First, multiply 125 × 82 (ignoring decimals for now): 125 × 80 = 10000 125 × 2 = 250 Add: 10000 + 250 = 10250 Now, since 12.5 has one decimal place and 8.2 has one decimal place, the product has two decimal places. So 12.5 × 8.2 = 102.50 Step 3: Multiply the result by the height. 102.50 × 15.7 First, multiply 10250 × 157 (ignoring decimals): 10250 × 100 = 1025000 10250 × 50 = 512500 10250 × 7 = 71750 Add: 1025000 + 512500 = 1537500 1537500 + 71750 = 1609250 Now, since 102.50 has two decimal places and 15.7 has one decimal place, the product has three decimal places. So 102.50 × 15.7 = 1609.250 Step 4: Write the final answer in cubic centimeters. Volume = 1609.25 cm³ (we can drop the trailing zero) Final Answer: 1609.25

2. A rectangular prism has a length of 8.5 cm, a width of 6.2 cm, and a height of 4.7 cm. What is the volume of this prism? Answer: 247.69 Solution: To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Write down the given dimensions. Length = 8.5 cm Width = 6.2 cm Height = 4.7 cm Substitute the values into the formula.
   Full step-by-step solution

   To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Step 1: Write down the given dimensions. Length = 8.5 cm Width = 6.2 cm Height = 4.7 cm Step 2: Substitute the values into the formula. Volume = 8.5 × 6.2 × 4.7 Step 3: First, multiply the length and the width. 8.5 × 6.2 To do this, first multiply 85 × 62 = 5270. Since 8.5 has one decimal place and 6.2 has one decimal place, the product must have two decimal places. So, 8.5 × 6.2 = 52.70 Step 4: Now multiply this result by the height. 52.70 × 4.7 First, multiply 5270 × 47. 5270 × 40 = 210800 5270 × 7 = 36890 Add them: 210800 + 36890 = 247690 Since 52.70 has two decimal places and 4.7 has one decimal place, the product must have three decimal places. So, 52.70 × 4.7 = 247.690 Step 5: Write the final answer with the correct unit. The volume is 247.69 cubic centimeters (since we typically round to two decimal places for consistency with the given measurements, 247.690 becomes 247.69). Final Answer: 247.69

3. Emma is tracking the growth of her sunflower plant for a science project. After 3 weeks, her plant has grown to a height of 1.875 meters. She needs to record this measurement rounded to the nearest tenth of a meter in her project journal. What height should Emma write down? Answer: 1.9 Solution: Identify the digit in the tenths place: 1.875 has 8 in the tenths place Look at the digit to the right (hundredths place): The hundredths digit is 7 Since 7 is greater than or equal to 5, we round the tenths place up 8 in the tenths place becomes 9, and all digits to the right become zero 1.875…
   Full step-by-step solution

   Step 1: Identify the digit in the tenths place: 1.875 has 8 in the tenths place Step 2: Look at the digit to the right (hundredths place): The hundredths digit is 7 Step 3: Since 7 is greater than or equal to 5, we round the tenths place up Step 4: 8 in the tenths place becomes 9, and all digits to the right become zero Step 5: 1.875 rounded to the nearest tenth is 1.9 The answer is 1.9.

4. Mere is baking cookies for a school fundraiser. Her digital kitchen scale shows that a bag of flour weighs 3.718 kilograms. The recipe calls for the flour to be measured to the nearest tenth of a kilogram. What weight should Mere record for the flour? Answer: 3.7 Solution: Identify the tenths place in 3.718. The tenths place is the first digit after the decimal point, which is 7. Look at the digit to the right of the tenths place, which is 1 (in the hundredths place).
   Full step-by-step solution

   Step 1: Identify the tenths place in 3.718. The tenths place is the first digit after the decimal point, which is 7. Step 2: Look at the digit to the right of the tenths place, which is 1 (in the hundredths place). Step 3: Since 1 is less than 5, we do not round up. The tenths digit stays 7. Step 4: All digits to the right of the tenths place become zero, so we get 3.700, which is written as 3.7. The answer is 3.7.

5. 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.