Introduction to Place Value
Learn what place value means and how each digit in a number has a specific value based on its position.
Definition
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| 1,000 | 100 | 10 | 1 |
- The 3 is in the thousands place, so it represents
- The 5 is in the hundreds place, so it represents
- The 2 is in the tens place, so it represents
- The 7 is in the ones place, so it represents
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Worked Examples
What is the value of the digit 6 in the number ?
Find the position of 6
Reading right to left: 3 is in ones, 4 is in tens, 6 is in hundreds → 6 is in the hundreds place
Calculate the value
→
Verify
→ The 6 represents 600
Answer: The digit 6 in has a value of .
Common Mistakes
Confusing the digit with its value (saying 5 instead of 500)
Why it's wrong: Students forget that position matters. The digit 5 in 1,523 is worth 500, not 5.
Correct: Always ask: What place is this digit in? Then multiply: digit × place value = value
Reading digits from left to right when identifying places
Why it's wrong: Place values are named from the right (ones, tens, hundreds...). Reading from the left can cause confusion.
Correct: Start from the rightmost digit (ones place) and work left: ones → tens → hundreds → thousands
Forgetting zeros in expanded form
Why it's wrong: In a number like 4,507, the 0 in the tens place is a placeholder and represents 0 × 10 = 0.
Correct: Zeros matter! 4,507 = 4,000 + 500 + 0 + 7 (though we often write 4,000 + 500 + 7)
Interactive Visual
Place Value Chart
| Thousands 1,000 | Hundreds 100 | Tens 10 | Ones 1 |
|---|---|---|---|
| 3 | 5 | 2 | 7 |
Expanded Form:
3 × 1,000 + 5 × 100 + 2 × 10 + 7 × 1
Click on any place value to highlight it and see its value.
Interactive Sandbox
Expression Calculator
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History
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Practice Problems
16 problemsIn the number , what position is the digit 5 in?
Why It Matters
- Read large numbers: Know what means versus
- Add and subtract: Line up digits correctly when calculating
- Understand money: A 10 dollar bill is worth ten 1 dollar bills
- Measure things: 100 centimeters equals 1 meter
Real World Applications
Money and Place Value
Our money system uses place value. Each larger bill is worth 10 times the smaller one.
Example:
If you have 3 hundred-dollar bills, 4 ten-dollar bills, and 7 one-dollar bills, you have 347 dollars.
A toy costs 285 dollars. You have 2 hundred-dollar bills, 7 ten-dollar bills, and 15 one-dollar bills.
Do you have enough money?
Step 1: Write the mathematical expression
Calculate your total:
Odometers in Cars
Car odometers show distance traveled using place value. Each digit represents a different unit.
Example:
If an odometer shows 12,345 km, the car has traveled 12 thousand kilometers, plus 345 more.
A car's odometer shows 8,067 km. The owner wants to know when it will reach 9,000 km.
How many more kilometers until 9,000?
Step 1: Write the mathematical expression
Calculate:
Key Takeaways
- 1Place value tells us the value of each digit based on its position in a number
- 2Each place is 10 times the value of the place to its right (ones → tens → hundreds → thousands)
- 3The same digit can have different values: 5 in 523 is worth 500, but 5 in 352 is worth 50
- 4Expanded form shows a number as the sum of each digit times its place value
Frequently Asked Questions
Glossary
- Place value
- The value of a digit based on its position in a number
- Digit
- The symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 used to write numbers
- Expanded form
- Writing a number as the sum of each digit times its place value (e.g., )
- Standard form
- The normal way of writing a number (e.g., )