Round Decimals

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Answer Key & Explanations

Round Decimals · Grade 4 · Worksheet 2

1. Sophia draws a large square on grid paper where each square unit represents 1 square meter. The side length of the square is 6.3 meters. She then shades a smaller square inside it with a side length of 2.6 meters. What is the area of the unshaded part of the large square? Round your answer to the nearest whole number. Answer: 33 Solution: Find the area of the large square. Area = side × side = 6.3 × 6.3. First, multiply 63 × 63 = 3969.
   Full step-by-step solution

   Step 1: Find the area of the large square. Area = side × side = 6.3 × 6.3. First, multiply 63 × 63 = 3969. Since there are 2 decimal places total, the area is 39.69 square meters. Step 2: Find the area of the small square. Area = 2.6 × 2.6. First, multiply 26 × 26 = 676. Since there are 2 decimal places total, the area is 6.76 square meters. Step 3: Subtract the small square's area from the large square's area: 39.69 - 6.76 = 32.93 square meters. Step 4: Round 32.93 to the nearest whole number. Look at the tenths digit: 9. Since 9 is greater than or equal to 5, round up. 32.93 rounds to 33. The answer is 33.

2. A rectangular garden has a length of 12.75 meters and a width of 8.35 meters. What is the area of the garden, rounded to the nearest tenth of a square meter? Answer: 106.5 Solution: We are given the length and width of a rectangular garden. Length = 12.75 m Width = 8.35 m We need to find the area and round it to the nearest tenth of a square meter.
   Full step-by-step solution

   Step 1: Understand the problem We are given the length and width of a rectangular garden. Length = 12.75 m Width = 8.35 m We need to find the area and round it to the nearest tenth of a square meter. Step 2: Recall the formula for area of a rectangle Area = length × width Step 3: Multiply the given numbers 12.75 × 8.35 First, break it down: 12.75 × 8.35 = 12.75 × (8 + 0.35) = (12.75 × 8) + (12.75 × 0.35) Step 4: Calculate 12.75 × 8 12.75 × 8 = 102.00 Step 5: Calculate 12.75 × 0.35 12.75 × 0.35 = 12.75 × (35/100) But let's multiply directly: 12.75 × 0.35 First, 12.75 × 0.3 = 3.825 Then, 12.75 × 0.05 = 0.6375 Add: 3.825 + 0.6375 = 4.4625 Step 6: Add the two parts 102.00 + 4.4625 = 106.4625 Step 7: Round to the nearest tenth 106.4625 Look at the hundredths digit: 6 (which is 5 or greater) So we round the tenths digit (4) up by 1 → 106.5 Step 8: Final answer Area = 106.5 square meters

3. Noah draws a number line from 0 to 10. He marks a point at 7.36. What is 7.36 rounded to the nearest whole number? Answer: 7 Solution: We need to round 7.36 to the nearest whole number. Step 2: Look at the digit in the tenths place, which is 3 (since 7.36 = 7 and 36 hundredths).
   Full step-by-step solution

   Step 1: We need to round 7.36 to the nearest whole number. Step 2: Look at the digit in the tenths place, which is 3 (since 7.36 = 7 and 36 hundredths). Step 3: The rule for rounding to the nearest whole number: if the tenths digit is 5 or greater, round up; if it is 4 or less, round down. Step 4: Here, the tenths digit is 3, which is less than 5, so we round down. Step 5: Rounding down means the whole number stays 7. Step 6: Therefore, 7.36 rounded to the nearest whole number is 7. The answer is 7.

4. Olivia is drawing a large square on a grid. The side length of the square is 3.7 units. She wants to round the side length to the nearest whole number to estimate the area. What is the side length rounded to the nearest whole number? Answer: 4 Solution: The side length is 3.7. To round to the nearest whole number, look at the tenths digit, which is 7. Step 2: Since 7 is greater than or equal to 5, we round up the whole number part from 3 to 4.
   Full step-by-step solution

   Step 1: The side length is 3.7. To round to the nearest whole number, look at the tenths digit, which is 7. Step 2: Since 7 is greater than or equal to 5, we round up the whole number part from 3 to 4. Step 3: The side length rounded to the nearest whole number is 4. The answer is 4.

5. Emma is baking cookies for her school bake sale. Her recipe calls for 2.25 cups of flour for chocolate chip cookies and 1.75 cups of flour for oatmeal raisin cookies. How many total cups of flour does Emma need for both types of cookies? Answer: 4.00 Solution: Identify the amounts needed: 2.25 cups for chocolate chip cookies and 1.75 cups for oatmeal raisin cookies.
   Full step-by-step solution

   Step 1: Identify the amounts needed: 2.25 cups for chocolate chip cookies and 1.75 cups for oatmeal raisin cookies. Step 2: Set up the addition problem: 2.25 + 1.75 Step 3: Line up the decimal points and add: 2.25 + 1.75 ------- Step 4: Add the hundredths place: 5 + 5 = 10, write 0 and carry over 1 to the tenths place Step 5: Add the tenths place: 2 + 7 + 1 (carried over) = 10, write 0 and carry over 1 to the ones place Step 6: Add the ones place: 2 + 1 + 1 (carried over) = 4 Step 7: The result is 4.00 Emma needs 4.00 cups of flour total.

6. Round 12.47 to the nearest tenth = ? Answer: 12.5 Solution: Identify the digit in the tenths place. In 12.47, the tenths digit is 4. Look at the digit immediately to the right (the hundredths place).
   Full step-by-step solution

   Step 1: Identify the digit in the tenths place. In 12.47, the tenths digit is 4. Step 2: Look at the digit immediately to the right (the hundredths place). In 12.47, the hundredths digit is 7. Step 3: Since the hundredths digit (7) is 5 or greater, we round the tenths digit (4) up by 1. This makes the tenths digit become 5. Step 4: All digits to the right of the tenths place become zero, so 12.47 becomes 12.50, which is written as 12.5. The answer is 12.5.