Expanded Form Calculator
Convert whole numbers and decimals to expanded form, expanded notation, power-of-10 form, and a place-value table.
Last Updated: May 2026
Enter one whole number or decimal. Commas and spaces are ignored.
Expanded form
5,000 + 800 + 20 + 9
Standard form
5,829
Power form
5 x 10^3 + 8 x 10^2 + 2 x 10^1 + 9 x 10^0
Nonzero places
4
| Digit | Place | Power | Place value | Expanded form status |
|---|---|---|---|---|
| 5 | thousands | 10^3 | 5,000 | Included |
| 8 | hundreds | 10^2 | 800 | Included |
| 2 | tens | 10^1 | 20 | Included |
| 9 | ones | 10^0 | 9 | Included |
Expanded form adds the nonzero place values. Zero place values are shown in the table but omitted from the sum.
Each row maps one digit to its place name, power of 10, and numeric place value.
Decimal digits use negative powers of 10: tenths are 10^-1, hundredths are 10^-2, and so on.
Place-Value Notice
This calculator is for finite decimal place-value work. It does not expand repeating decimals or symbolic expressions, and it limits input length to keep the table readable.
Checked by Jitendra Kumar
Expanded Form Calculator is checked for formula labels, source links, and result limits.
Jitendra Kumar, Founder & Editorial Standards Lead. Updated May 2026. Scope: math calculators.
How to Use the Expanded Form Calculator
Enter one whole number or decimal. You can include commas or spaces in pasted numbers; the calculator removes them before reading the digits.
Read the expanded addition form first, then use the power form and place-value table to see how each digit maps to a power of 10.
Step 1: Enter a number
Use one whole number or terminating decimal.
Step 2: Read expanded form
The highlighted result writes the number as a sum of nonzero place values.
Step 3: Compare power form
The power form writes each nonzero digit as digit x 10^place.
Step 4: Audit the place table
Use the table to see every digit, including zeros that are omitted from the sum.
How This Expanded Form Calculator Works
The calculator reads the number as a base-10 digit string. Each digit receives a power of 10 based on its position relative to the decimal point.
Digits left of the decimal point use nonnegative powers: ones are 10^0, tens are 10^1, hundreds are 10^2, and so on. Digits right of the decimal point use negative powers: tenths are 10^-1, hundredths are 10^-2, and so on.
The expanded addition form includes only nonzero place values. The place-value table still shows zero digits so the original number can be checked digit by digit.
Expanded Form Guide
Core Expanded Form Rules
| Concept | Rule | Use |
|---|---|---|
| Expanded form | number = sum of nonzero place values | Shows what each digit contributes. |
| Power form | digit x 10^place | Connects each digit to a power of 10. |
| Ones place | 10^0 = 1 | The anchor place immediately left of the decimal point. |
| Decimal places | tenths = 10^-1, hundredths = 10^-2 | Uses negative powers of 10. |
| Zero digits | 0 x place value = 0 | Usually omitted from the expanded sum. |
Expanded Form Examples
| Number | Expanded form | Power form note |
|---|---|---|
| 5,829 | 5,000 + 800 + 20 + 9 | 5 x 10^3 + 8 x 10^2 + 2 x 10^1 + 9 x 10^0 |
| 407.305 | 400 + 7 + 0.3 + 0.005 | 4 x 10^2 + 7 x 10^0 + 3 x 10^-1 + 5 x 10^-3 |
| 0.0625 | 0.06 + 0.002 + 0.0005 | 6 x 10^-2 + 2 x 10^-3 + 5 x 10^-4 |
| -348.19 | -300 - 40 - 8 - 0.1 - 0.09 | Negative sign applies to the full place-value sum. |
Place-Value Context
Expanded form is useful for learning place value, checking decimal understanding, comparing numbers, decomposing arithmetic problems, and connecting standard notation to powers of 10.
Keep the research moving with Long Addition Calculator, Long Subtraction Calculator, Scientific Notation Calculator, and Integer Calculator.
Frequently Asked Questions
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- 1.Wolfram MathWorld - Expanded Notation(Accessed May 2026)
- 2.Wolfram MathWorld - Decimal Expansion(Accessed May 2026)
- 3.Khan Academy - Decimals in Expanded Form Review(Accessed May 2026)