Expanded Form of Numbers
When we write a number in expanded form, we break it apart to show the value that each digit contributes. Expanded form makes the structure of a number visible and reinforces understanding of place value.
What Is Expanded Form?
Expanded form expresses a number as the sum of each digit multiplied by its place value.
4,736 = 4,000 + 700 + 30 + 6
Steps to Write Expanded Form
- Identify the place value of each digit.
- Multiply each digit by its place value to find its contribution.
- Write all contributions joined by + signs.
- Skip zeros – a zero digit contributes nothing.
Worked Examples
| Number | Expanded Form |
|---|---|
| 52 | 50 + 2 |
| 308 | 300 + 8 |
| 5,029 | 5,000 + 20 + 9 |
| 47,600 | 40,000 + 7,000 + 600 |
| 2,000,305 | 2,000,000 + 300 + 5 |
Expanded Form Using Multiplication
A more formal version writes each digit multiplied by its place value:
3,482 = (3 × 1,000) + (4 × 100) + (8 × 10) + (2 × 1)
Expanded Notation with Powers of 10
At a higher level, place values are written as powers of 10:
3,482 = (3 × 10³) + (4 × 10²) + (8 × 10¹) + (2 × 10⁰)
Expanded Form for Decimals
12.35 = 10 + 2 + 0.3 + 0.05
| Digit | Place | Value |
|---|---|---|
| 1 | Tens | 10 |
| 2 | Ones | 2 |
| 3 | Tenths | 0.3 |
| 5 | Hundredths | 0.05 |
Key Points
- Expanded form shows the value contributed by each digit.
- Zeros do not need to be written in expanded form as they contribute nothing.
- The multiplication version uses each digit times its place value.
- The power-of-10 version replaces place values with exponents.
- Expanded form works for decimals as well as whole numbers.
Quick Practice
- Write 7,053 in expanded form.
- Write 430,007 in expanded form using multiplication notation.
- Convert 60,000 + 400 + 9 back to standard form.
- Write 5.07 in expanded form.
- Express 2,800,050 in expanded form with powers of 10.
Summary
Expanded form unpacks a number to reveal the individual contribution of each digit. It is a bridge between a numeral and the underlying place value concept, and is foundational to understanding arithmetic, algebraic expressions, and polynomial notation in higher mathematics.