Place Value (Through Hundred Thousands) for 4th Grade
Place value is the foundation of our number system. In Grade 4, students work with numbers through hundred thousands and understand that each digit has a value based on its position in the number. Without a solid grasp of place value, fourth graders struggle with comparing numbers, rounding, and adding or subtracting large numbers correctly.
Our number system is base-ten. That means each place is 10 times the value of the place to its right. From right to left we have: ones (1), tens (10), hundreds (100), thousands (1,000), ten thousands (10,000), and hundred thousands (100,000). We use commas to separate groups of three digits so that numbers like 356,824 are easier to read and write.
DETAILED EXPLANATION
In a number like 427,536, each digit has a specific value. The 4 is in the hundred thousands place, so it represents 400,000. The 2 is in the ten thousands place (20,000), the 7 is in the thousands place (7,000), the 5 is in the hundreds place (500), the 3 is in the tens place (30), and the 6 is in the ones place (6). The total value of the number is the sum of all these: 400,000 + 20,000 + 7,000 + 500 + 30 + 6.
Expanded form writes a number as the sum of each digit’s value. For example, 52,341 in expanded form is 50,000 + 2,000 + 300 + 40 + 1. Standard form is the usual way we write numbers (52,341). Word form uses words (fifty-two thousand, three hundred forty-one). Being able to move between these forms helps students understand what each digit means.
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WORKED EXAMPLES WITH STEP BY STEP SOLUTIONS
Example 1
Write 427,536 in expanded form.
Solutions:
Step 1: Identify the value of each digit. 4 is in the hundred thousands place = 400,000. 2 is in the ten thousands place = 20,000. 7 is in the thousands place = 7,000. 5 is in the hundreds place = 500. 3 is in the tens place = 30. 6 is in the ones place = 6.
Step 2: Write the expanded form as a sum: 400,000 + 20,000 + 7,000 + 500 + 30 + 6.
Answer: 427,536 = 400,000 + 20,000 + 7,000 + 500 + 30 + 6.
Example 2
Write 300,000 + 80,000 + 5,000 + 200 + 40 + 9 in standard form.
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Solutions:
Step 1: Line up the values by place. Hundred thousands: 3. Ten thousands: 8. Thousands: 5. Hundreds: 2. Tens: 4. Ones: 9.
Step 2: Write the number with a comma after the thousands: 385,249.
Answer: 385,249
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