Expanded Form
Learn how to write numbers in expanded form by breaking them down into place values.
Definition
- The 3 is in the thousands place, so its value is
- The 5 is in the hundreds place, so its value is
- The 2 is in the tens place, so its value is
- The 7 is in the ones place, so its value is
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Worked Examples
Write in expanded form.
Identify each digit's place value
4 is in hundreds, 8 is in tens, 5 is in ones → Places identified
Write the value of the hundreds digit
→
Write the value of the tens digit
→
Write the value of the ones digit
→
Connect with addition signs
→ Expanded form complete
Answer:
Common Mistakes
Writing just the digit instead of its value (e.g., writing for )
Why it's wrong: Each digit has a different value based on its position. The 3 in 3,527 is not worth 3, it's worth 3,000!
Correct: Multiply each digit by its place value:
Including zero values (e.g., writing )
Why it's wrong: Adding zero doesn't change the sum, so we typically skip it to keep expanded form clean.
Correct: Just write (skip the zero in the tens place)
Mixing up place values (e.g., thinking tens come before hundreds)
Why it's wrong: Place values go right to left: ones, tens, hundreds, thousands, etc.
Correct: From right to left: ones (1), tens (10), hundreds (100), thousands (1,000)
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
17 problemsWhat is the expanded form of ?
Why It Matters
- See the value of each digit: Know that the 5 in 523 means 500, not just 5
- Add and subtract more easily: Break large numbers into manageable parts
- Understand place value deeply: See how our number system is built on powers of 10
- Compare numbers: Quickly see which number is larger by comparing place values
Real World Applications
Counting Money
When you count money, you naturally use expanded form thinking.
Example:
If you have 2 hundred-dollar bills, 3 ten-dollar bills, and 4 one-dollar bills, that's dollars.
You have 5 hundred-dollar bills, 0 ten-dollar bills, and 8 one-dollar bills.
How much money do you have in total?
Step 1: Write the mathematical expression
Write in expanded form first:
Reading Large Numbers
Expanded form helps you understand large numbers like distances or populations.
Example:
A city has a population of . That's people.
A road trip is kilometers long.
Write this distance in expanded form.
Step 1: Write the mathematical expression
Break down :
Key Takeaways
- 1Expanded form shows a number as the sum of the values of each digit
- 2Each digit's value depends on its place: ones, tens, hundreds, thousands
- 3To find a digit's value, multiply it by its place value
- 4We skip zeros in expanded form since they add nothing to the sum
- 5Expanded form and standard form represent the same number in different ways
Frequently Asked Questions
Glossary
- Expanded form
- A way of writing a number that shows the value of each digit added together
- Standard form
- The regular way of writing a number (e.g., )
- Place value
- The value of a digit based on its position in a number
- Digit
- A single symbol used to write numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)