Expanded Form Calculator
Write a number as the sum of its place values, in all three forms schools use — and in words.
Expanded form separates a number into what each digit contributes.
How the expanded form calculator works
Expanded form separates a number into what each digit contributes. There are three conventions and schools differ on which they ask for:
Expanded form adds the place values: 4,530 = 4000 + 500 + 30. Expanded factor form shows the multiplication: (4 × 1000) + (5 × 100) + (3 × 10). Expanded exponential form uses powers of ten: (4 × 10³) + (5 × 10²) + (3 × 10¹).
All three say the same thing; the exponential one makes the pattern of the place values explicit, which is why it appears once powers are taught.
Formula: n = Σ (digit × 10^place)
Worked examples
| Inputs | Expanded form | Note |
|---|---|---|
| 4,530 in expanded form | 4000 + 500 + 30 | 4000 + 500 + 30 |
| A number with zeros | 2000 + 20 + 5 | 2000 + 20 + 5 |
| Six digits | 300000 + 5000 + 70 | 300000 + 5000 + 70 |
FAQFrequently asked questions
What is expanded form?
A number written as the sum of what each digit is worth: 4,530 = 4000 + 500 + 30.
What is expanded factor form?
The same thing showing the multiplication: (4 × 1000) + (5 × 100) + (3 × 10).
What is expanded exponential form?
The factor form with powers of ten: (4 × 10³) + (5 × 10²) + (3 × 10¹).
What happens to zeros?
They contribute nothing, so they are left out of the expansion — 2,025 is 2000 + 20 + 5.
Why teach it?
Because it makes place value explicit, which is what every written arithmetic method depends on.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.