Place Value to Millions

lessonbunny.com

Answer Key & Explanations

Place Value to Millions · Grade 4 · Worksheet 2

1. A city library received a donation of 4,250 books. They already had 8,975 books in their collection. After the donation, how many books does the library have in total? Answer: 13225 Solution: Identify the numbers involved. The library originally had 8,975 books. They received a donation of 4,250 books.
   Full step-by-step solution

   Step 1: Identify the numbers involved. The library originally had 8,975 books. They received a donation of 4,250 books. Step 2: Understand what to do. To find the total number of books after the donation, we need to add the original number of books to the donated books. So, the operation is: 8,975 + 4,250 Step 3: Add the numbers step by step. We can add by aligning the digits by place value: Write them one below the other: 8 9 7 5 + 4 2 5 0 Step 4: Start adding from the rightmost column (ones place): 5 + 0 = 5 Write 5 in the ones place of the answer. Step 5: Move to the tens place: 7 + 5 = 12 Write 2 in the tens place, and carry over 1 to the hundreds place. Step 6: Add the hundreds place (including carry): 9 + 2 = 11, plus the carried 1 makes 12 Write 2 in the hundreds place, and carry over 1 to the thousands place. Step 7: Add the thousands place (including carry): 8 + 4 = 12, plus the carried 1 makes 13 Write 3 in the thousands place, and 1 in the ten-thousands place. Step 8: Write the final number from left to right: 13,225 Step 9: Check the result: 8,975 + 4,250 = 13,225 Thus, after the donation, the library has 13,225 books in total.

2. Aroha is looking at a place value chart shaped like a staircase. The chart has seven steps, each labeled with a place value from ones to millions. On the chart, a digit 7 is placed on the hundred thousands step, a digit 3 is on the ten thousands step, a digit 5 is on the thousands step, a digit 9 is on the hundreds step, a digit 1 is on the tens step, and a digit 7 is on the ones step. What is the value of the digit in the hundred thousands place? Answer: 700,000 Solution: Identify the digit in the hundred thousands place: 7. The hundred thousands place means 7 groups of one hundred thousand. 7 x 100,000 = 700,000.
   Full step-by-step solution

   Step 1: Identify the digit in the hundred thousands place: 7. Step 2: The hundred thousands place means 7 groups of one hundred thousand. Step 3: 7 x 100,000 = 700,000. The answer is 700,000.

3. 6,205,830 × 10 = ? Answer: 62,058,300 Solution: Start with 6,205,830 Multiplying by 10 means each digit moves one place to the left. The 6 in the millions place becomes 6 in the ten-millions place. The 2 in the hundred-thousands place becomes 2 in the millions place.
   Full step-by-step solution

   Step 1: Start with 6,205,830 Step 2: Multiplying by 10 means each digit moves one place to the left. Step 3: The 6 in the millions place becomes 6 in the ten-millions place. Step 4: The 2 in the hundred-thousands place becomes 2 in the millions place. Step 5: The 0 in the ten-thousands place becomes 0 in the hundred-thousands place. Step 6: The 5 in the thousands place becomes 5 in the ten-thousands place. Step 7: The 8 in the hundreds place becomes 8 in the thousands place. Step 8: The 3 in the tens place becomes 3 in the hundreds place. Step 9: The 0 in the ones place becomes 0 in the tens place. Step 10: A zero is added in the ones place. Step 11: The result is 62,058,300. The answer is 62,058,300.

4. 3,456,789 - 1,234,567 = ? Answer: 2222222 Solution: 3,456,789 − 1,234,567 3,456,789 − 1,234,567 9 − 7 = 2 So, the ones digit of the answer is 2. 8 − 6 = 2 So, the tens digit is 2. 7 − 5 = 2 So, the hundreds digit is 2.
   Full step-by-step solution

   Let's subtract step-by-step. We have: 3,456,789 − 1,234,567 --- **Step 1: Write the numbers aligned by place value** Imagine writing them one under the other: ``` 3,456,789 − 1,234,567 ----------- ``` --- **Step 2: Subtract units (ones) place** 9 − 7 = 2 So, the ones digit of the answer is 2. --- **Step 3: Subtract tens place** 8 − 6 = 2 So, the tens digit is 2. --- **Step 4: Subtract hundreds place** 7 − 5 = 2 So, the hundreds digit is 2. --- **Step 5: Subtract thousands place** 6 − 4 = 2 So, the thousands digit is 2. --- **Step 6: Subtract ten-thousands place** 5 − 3 = 2 So, the ten-thousands digit is 2. --- **Step 7: Subtract hundred-thousands place** 4 − 2 = 2 So, the hundred-thousands digit is 2. --- **Step 8: Subtract millions place** 3 − 1 = 2 So, the millions digit is 2. --- **Step 9: Combine the digits** We got 2 (millions), 2 (hundred-thousands), 2 (ten-thousands), 2 (thousands), 2 (hundreds), 2 (tens), 2 (ones). That is: 2,222,222 --- **Final Answer:** 2222222

5. 4,376,521 - 2,189,407 = ? Answer: 2187114 Solution: 4,376,521 - 2,189,407 We subtract from rightmost digit to left. 1 - 7: cannot do directly, so borrow from the tens place. Tens digit is 2, but it's 0 after borrowing?
   Full step-by-step solution

   Let's subtract step-by-step: 4,376,521 - 2,189,407. We align the numbers by place value: 4,376,521 - 2,189,407 ------------ We subtract from rightmost digit to left. **Step 1: Ones place** 1 - 7: cannot do directly, so borrow from the tens place. Tens digit is 2, but it's 0 after borrowing? Let's carefully borrow across zeros. Actually, let's borrow systematically: Write 4,376,521 as: Millions: 4 Hundred-thousands: 3 Ten-thousands: 7 Thousands: 6 Hundreds: 5 Tens: 2 Ones: 1 We start subtraction in the ones column: Ones: 1 - 7 → need to borrow from the tens place. Tens place is 2. Borrow 1 ten from tens place (2 becomes 1), giving 10 + 1 = 11 ones. 11 - 7 = 4. Ones digit result: 4. **Step 2: Tens place** After borrowing, tens digit was 2, now it's 1 (because we borrowed 1 ten for the ones column). 1 - 0 = 1. Tens digit result: 1. **Step 3: Hundreds place** 5 - 4 = 1. Hundreds digit result: 1. **Step 4: Thousands place** 6 - 9: cannot do, borrow from ten-thousands place. Ten-thousands digit is 7. Borrow 1 from 7 → 7 becomes 6, and 6 thousands becomes 16 thousands. 16 - 9 = 7. Thousands digit result: 7. **Step 5: Ten-thousands place** After borrowing, ten-thousands digit is 6. 6 - 8: cannot do, borrow from hundred-thousands place. Hundred-thousands digit is 3. Borrow 1 from 3 → 3 becomes 2, and 6 ten-thousands becomes 16 ten-thousands. 16 - 8 = 8. Ten-thousands digit result: 8. **Step 6: Hundred-thousands place** After borrowing, hundred-thousands digit is 2. 2 - 1 = 1. Hundred-thousands digit result: 1. **Step 7: Millions place** 4 - 2 = 2. Millions digit result: 2. So the result digits from left to right: Millions: 2 Hundred-thousands: 1 Ten-thousands: 8 Thousands: 7 Hundreds: 1 Tens: 1 Ones: 4 That gives: 2,187,114. Final answer: 2187114

6. Mason is helping his school library organize their new book donations. They received 1,247,582 fiction books, 987,427 non-fiction books, and 112,347 reference books. What is the total number of books the library received? Answer: 2,347,356 Solution: Write the numbers aligned by place value (ones, tens, hundreds, thousands, etc.): 1,247,582 987,427 + 112,347 Add the ones column: 2 + 7 + 7 = 16 (write 6, carry 1 to the tens column).
   Full step-by-step solution

   Step 1: Write the numbers aligned by place value (ones, tens, hundreds, thousands, etc.): 1,247,582 987,427 + 112,347 Step 2: Add the ones column: 2 + 7 + 7 = 16 (write 6, carry 1 to the tens column). Step 3: Add the tens column: 8 + 2 + 4 + 1 (carry) = 15 (write 5, carry 1 to the hundreds column). Step 4: Add the hundreds column: 5 + 4 + 3 + 1 (carry) = 13 (write 3, carry 1 to the thousands column). Step 5: Add the thousands column: 7 + 7 + 2 + 1 (carry) = 17 (write 7, carry 1 to the ten thousands column). Step 6: Add the ten thousands column: 4 + 8 + 1 + 1 (carry) = 14 (write 4, carry 1 to the hundred thousands column). Step 7: Add the hundred thousands column: 2 + 9 + 1 + 1 (carry) = 13 (write 3, carry 1 to the millions column). Step 8: Add the millions column: 1 + 0 + 0 + 1 (carry) = 2. Step 9: The total is 2,347,356. The answer is 2,347,356.

7. Kaia is helping her town plan a new nature reserve. The reserve will have three different habitat zones. The forest zone will cover 2,468,024 square meters, the wetland zone will cover 1,532,176 square meters, and the grassland zone will cover 987,615 square meters. What is the total area of the nature reserve in square meters? Answer: 4987815 Solution: Write the numbers aligned by place value, adding commas for clarity: 2,468,024 1,532,176 + 987,615 Add the ones column: 4 + 6 + 5 = 15. Write 5 in the ones place, carry 1 to the tens column.
   Full step-by-step solution

   Step 1: Write the numbers aligned by place value, adding commas for clarity: 2,468,024 1,532,176 + 987,615 Step 2: Add the ones column: 4 + 6 + 5 = 15. Write 5 in the ones place, carry 1 to the tens column. Step 3: Add the tens column: 2 + 7 + 1 + 1 (carry) = 11. Write 1 in the tens place, carry 1 to the hundreds column. Step 4: Add the hundreds column: 0 + 1 + 6 + 1 (carry) = 8. Write 8 in the hundreds place. Step 5: Add the thousands column: 8 + 2 + 7 = 17. Write 7 in the thousands place, carry 1 to the ten thousands column. Step 6: Add the ten thousands column: 6 + 3 + 8 + 1 (carry) = 18. Write 8 in the ten thousands place, carry 1 to the hundred thousands column. Step 7: Add the hundred thousands column: 4 + 5 + 9 + 1 (carry) = 19. Write 9 in the hundred thousands place, carry 1 to the millions column. Step 8: Add the millions column: 2 + 1 + 0 + 1 (carry) = 4. Write 4 in the millions place. Step 9: The total is 4,987,815 square meters. The answer is 4987815.

8. 4,327,156 - 2,918,049 = ? Answer: 1,409,107 Solution: 4,327,156 - 2,918,049 We start from the rightmost digit (ones place) and move left. 6 - 9: We can't do 6 - 9 directly, so we borrow 1 from the tens place. The 5 in the tens place becomes 4, and the 6 becomes 16.
   Full step-by-step solution

   Let's subtract 2,918,049 from 4,327,156 step by step. We write the numbers aligned by place value: 4,327,156 - 2,918,049 ------------ We start from the rightmost digit (ones place) and move left. **Step 1: Ones place** 6 - 9: We can't do 6 - 9 directly, so we borrow 1 from the tens place. The 5 in the tens place becomes 4, and the 6 becomes 16. 16 - 9 = 7 Write 7 in ones place. **Step 2: Tens place** After borrowing, tens digit is 4 (from 5 → 4). 4 - 4 = 0 Write 0 in tens place. **Step 3: Hundreds place** 1 - 0 = 1 Write 1 in hundreds place. **Step 4: Thousands place** 7 - 8: We can't do 7 - 8, so borrow 1 from the ten-thousands place. The 2 in the ten-thousands place becomes 1, and the 7 becomes 17. 17 - 8 = 9 Write 9 in thousands place. **Step 5: Ten-thousands place** After borrowing, ten-thousands digit is 1 (from 2 → 1). 1 - 1 = 0 Write 0 in ten-thousands place. **Step 6: Hundred-thousands place** 3 - 9: We can't do 3 - 9, so borrow 1 from the millions place. The 4 in millions place becomes 3, and the 3 becomes 13. 13 - 9 = 4 Write 4 in hundred-thousands place. **Step 7: Millions place** After borrowing, millions digit is 3 (from 4 → 3). 3 - 2 = 1 Write 1 in millions place. Now we have the result: 1,409,107. Let's check quickly: 4,327,156 - 2,918,049 = (4,327,156 - 2,000,000) = 2,327,156 2,327,156 - 900,000 = 1,427,156 1,427,156 - 18,000 = 1,409,156 1,409,156 - 49 = 1,409,107 Yes, it matches. Final answer: 1,409,107