Expanded Form Calculator
Enter a whole number below to instantly break it into place-value terms.
How Expanded Form Works
Each digit's place value is the digit multiplied by its power of ten (ones, tens, hundreds, and so on). Adding all the place values back together reproduces the original number.
Expanded form extends past the ones place, too. Place values continue as tenths, hundredths, and so on for decimals — 3.42 in expanded form is 3 + 0.4 + 0.02, since the 4 is in the tenths place (4 × 0.1) and the 2 is in the hundredths place (2 × 0.01).
Worked example
Write 4,025 in expanded form.
4 is in the thousands place: 4,000. 2 is in the tens place: 20. 5 is in the ones place: 5.
Expanded form: 4,000 + 20 + 5
A second example, with a zero digit in the middle: write 10,506 in expanded form.
1 is in the ten-thousands place: 10,000. The 0 in the thousands place is dropped. 5 is in the hundreds place: 500. The 0 in the tens place is dropped. 6 is in the ones place: 6.
Expanded form: 10,000 + 500 + 6
Common mistake
A common mistake is including a zero place value in the sum, writing something like 4,000 + 0 + 20 + 5 for 4,025. A 0 digit contributes nothing, so its term should be dropped entirely rather than written out.
Keep going
- Expanded form and scientific notation both work from a number's place values, just in opposite directions; the scientific notation calculator compresses it back down instead. Scientific Notation Calculator
- Expanded form writes out the sum a place value chart shows visually; the place value chart lines a number's digits up under their columns instead of adding them together. Place Value Chart Calculator
Frequently Asked Questions
What is expanded form?
Expanded form breaks a number into the sum of the place value of each digit. For example, 4,025 in expanded form is 4,000 + 20 + 5.
Why do zero digits disappear in expanded form?
A zero digit contributes nothing to the sum (its place value is 0), so it's normally left out of the expanded form entirely.
How is expanded form useful?
It shows exactly what each digit in a number is worth, which is why it's commonly taught alongside place value in elementary math.
Does expanded form work with decimals?
Yes. Place values continue past the decimal point as tenths, hundredths, and so on. 6.19 in expanded form is 6 + 0.1 + 0.09.
Can expanded form be written using multiplication instead of just addition?
Yes — a more detailed version shows each digit times its place value before adding: 4,025 can be written as (4 × 1,000) + (2 × 10) + (5 × 1), which is the same idea with the multiplication made explicit.
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