Place Value Decimals

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Place Value Decimals · Grade 5 · Worksheet 2

1. Mere is measuring the mass of three different types of seeds for a school project. A sunflower seed has a mass of 0.047 grams, a pumpkin seed has a mass of 0.236 grams, and a chia seed has a mass of 0.008 grams. What is the digit in the thousandths place of the sunflower seed's mass? Answer: 7 Solution: Write the sunflower seed's mass: 0.047 grams. Step 2: Identify the decimal places: The first digit after the decimal point (0) is in the tenths place. The second digit (4) is in the hundredths place.
   Full step-by-step solution

   Step 1: Write the sunflower seed's mass: 0.047 grams. Step 2: Identify the decimal places: The first digit after the decimal point (0) is in the tenths place. The second digit (4) is in the hundredths place. The third digit (7) is in the thousandths place. Step 3: The digit in the thousandths place is 7. The answer is 7.

2. Write 9.631 in expanded form. Answer: 9 + 0.6 + 0.03 + 0.001 Solution: Identify the place value of each digit in 9.631.
   Full step-by-step solution

   Step 1: Identify the place value of each digit in 9.631. - The digit 9 is in the ones place: 9 × 1 = 9 - The digit 6 is in the tenths place: 6 × 0.1 = 0.6 - The digit 3 is in the hundredths place: 3 × 0.01 = 0.03 - The digit 1 is in the thousandths place: 1 × 0.001 = 0.001 Step 2: Write the expanded form as a sum of these values: 9 + 0.6 + 0.03 + 0.001 The answer is 9 + 0.6 + 0.03 + 0.001.

3. What is the value of the digit 7 in the number 8.537? Answer: 0.007 Solution: Write the number 8.537 and label each digit's place value. The digits to the right of the decimal point are: 5 (tenths), 3 (hundredths), 7 (thousandths). The digit 7 is in the thousandths place.
   Full step-by-step solution

   Step 1: Write the number 8.537 and label each digit's place value. Step 2: The digits to the right of the decimal point are: 5 (tenths), 3 (hundredths), 7 (thousandths). Step 3: The digit 7 is in the thousandths place. Step 4: The value of a digit in the thousandths place is the digit times 0.001. Step 5: 7 × 0.001 = 0.007. The answer is 0.007.

4. 0.375 + 0.642 = ? Answer: 1.017 Solution: Write the numbers aligned by their decimal points in your mind: 0.375 + 0.642 Start adding from the rightmost digit (thousandths place). Thousandths place: 5 + 2 = 7 Write 7 in the thousandths place.
   Full step-by-step solution

   Let's add 0.375 and 0.642 step by step. Step 1: Write the numbers aligned by their decimal points in your mind: 0.375 + 0.642 Step 2: Start adding from the rightmost digit (thousandths place). Thousandths place: 5 + 2 = 7 Write 7 in the thousandths place. Step 3: Move left to the hundredths place: 7 + 4 = 11 Write 1 in the hundredths place, and carry over 1 to the tenths place. Step 4: Tenths place: 3 + 6 = 9, plus the carried-over 1 = 10 Write 0 in the tenths place, and carry over 1 to the ones place. Step 5: Ones place: 0 + 0 = 0, plus the carried-over 1 = 1 Write 1 in the ones place. Step 6: Combine all digits: Ones place: 1 Tenths place: 0 Hundredths place: 1 Thousandths place: 7 So the result is 1.017. Final answer: 1.017

5. Liam is helping his father measure ingredients for a science experiment. They need 0.875 liters of water, 0.125 liters of oil, and 0.375 liters of vinegar. What is the total volume of liquid Liam and his father will have in liters? Answer: 1.375 Solution: Write the three amounts lined up by decimal point: 0.875 0.125 + 0.375 Add the thousandths place: 5 + 5 + 5 = 15. Write 5 in thousandths, carry 1 to hundredths. Add the hundredths place: 7 + 2 + 7 + 1 (carried) = 17.
   Full step-by-step solution

   Step 1: Write the three amounts lined up by decimal point: 0.875 0.125 + 0.375 Step 2: Add the thousandths place: 5 + 5 + 5 = 15. Write 5 in thousandths, carry 1 to hundredths. Step 3: Add the hundredths place: 7 + 2 + 7 + 1 (carried) = 17. Write 7 in hundredths, carry 1 to tenths. Step 4: Add the tenths place: 8 + 1 + 3 + 1 (carried) = 13. Write 3 in tenths, carry 1 to ones. Step 5: Add the ones place: 0 + 0 + 0 + 1 (carried) = 1. Write 1 in ones. Step 6: The total is 1.375 liters. The answer is 1.375.

6. Emma is building a model bridge for her science project. She needs to cut a wooden beam that is 2.875 meters long into 5 equal pieces. What will be the length of each piece in meters? Answer: 0.575 Solution: Start with the total length: 2.875 meters Divide by 5 to find the length of each piece: 2.875 ÷ 5 Set up the division: 5 into 2.875 5 goes into 2 zero times, so write 0 and bring down the decimal point 5 goes into 28 five times (5 × 5 = 25), write 5 after the decimal point Subtract: 28 - 25 = 3,…
   Full step-by-step solution

   Step 1: Start with the total length: 2.875 meters Step 2: Divide by 5 to find the length of each piece: 2.875 ÷ 5 Step 3: Set up the division: 5 into 2.875 Step 4: 5 goes into 2 zero times, so write 0 and bring down the decimal point Step 5: 5 goes into 28 five times (5 × 5 = 25), write 5 after the decimal point Step 6: Subtract: 28 - 25 = 3, bring down the 7 to make 37 Step 7: 5 goes into 37 seven times (5 × 7 = 35), write 7 Step 8: Subtract: 37 - 35 = 2, bring down the 5 to make 25 Step 9: 5 goes into 25 five times (5 × 5 = 25), write 5 Step 10: The result is 0.575 Each piece will be 0.575 meters long.

7. Write 9.847 in expanded form. Answer: 9 + 0.8 + 0.04 + 0.007 Solution: Identify the place value of each digit in 9.847.
   Full step-by-step solution

   Step 1: Identify the place value of each digit in 9.847. - The digit 9 is in the ones place: 9 × 1 = 9 - The digit 8 is in the tenths place: 8 × 0.1 = 0.8 - The digit 4 is in the hundredths place: 4 × 0.01 = 0.04 - The digit 7 is in the thousandths place: 7 × 0.001 = 0.007 Step 2: Write the sum of these values: 9 + 0.8 + 0.04 + 0.007 The answer is 9 + 0.8 + 0.04 + 0.007.

8. Emma is building a model bridge for her science project. She needs to cut three wooden beams to exact lengths. The first beam should be 1.375 meters long, the second beam should be 0.625 meters shorter than the first beam, and the third beam should be exactly halfway between the lengths of the first two beams. What is the length of the third beam in meters? Answer: 1.0625 Solution: First beam = 1.375 meters Second beam is 0.625 meters shorter than first beam Second beam = 1.375 - 0.625 = 0.75 meters Find the length halfway between first and second beams To find the middle point between two values, add them together and divide by 2 (1.375 + 0.75) ÷ 2 = 2.125 ÷ 2 = 1.0625…
   Full step-by-step solution

   Step 1: Find the length of the second beam First beam = 1.375 meters Second beam is 0.625 meters shorter than first beam Second beam = 1.375 - 0.625 = 0.75 meters Step 2: Find the length halfway between first and second beams To find the middle point between two values, add them together and divide by 2 (1.375 + 0.75) ÷ 2 = 2.125 ÷ 2 = 1.0625 meters Step 3: Verify the calculation 1.375 + 0.75 = 2.125 2.125 ÷ 2 = 1.0625 The third beam should be 1.0625 meters long.

9. 0.456 × 0.75 = ? Answer: 0.342 Solution: Multiply the numbers as if they were whole numbers: 456 × 75. Calculate 456 × 75 = 456 × (70 + 5) = (456 × 70) + (456 × 5) = 31920 + 2280 = 34200.
   Full step-by-step solution

   Step 1: Multiply the numbers as if they were whole numbers: 456 × 75. Step 2: Calculate 456 × 75 = 456 × (70 + 5) = (456 × 70) + (456 × 5) = 31920 + 2280 = 34200. Step 3: Count the total decimal places in the original factors: 0.456 has 3 decimal places, and 0.75 has 2 decimal places, so the total is 3 + 2 = 5 decimal places. Step 4: Place the decimal point in the product (34200) so that it has 5 decimal places: 0.34200. Step 5: Simplify by removing the trailing zeros: 0.34200 becomes 0.342. The answer is 0.342.