Expanded Form Calculator
The expanded form calculator writes a number as the sum of what each digit is worth, and lists each digit's place value beside it.
Expanded form
- Expanded notation Each digit times the value of its place.
- (3 × 10,000) + (5 × 100) + (2 × 10) + (7 × 1) + (8 × 0.01)
- Exponential form The place values as powers of ten: 10⁰ is the ones place, and negative powers are the places after the decimal point.
- (3 × 10⁴) + (5 × 10²) + (2 × 10¹) + (7 × 10⁰) + (8 × 10⁻²)
- With fractions The decimal places as tenths, hundredths and so on.
- (3 × 10,000) + (5 × 100) + (2 × 10) + (7 × 1) + (8 × 1/100)
- Zeros
- 2 zero digits, each worth 0, so left out of the sum
- Standard form
- 30,527.08
| Digit | Place | Value |
|---|---|---|
| 3 | ten thousands | 30,000 |
| 0 | thousands | 0 |
| 5 | hundreds | 500 |
| 2 | tens | 20 |
| 7 | ones | 7 |
| 0 | tenths | 0 |
| 8 | hundredths | 0.08 |
How the Expanded Form Calculator works
To write the expanded form of a number, multiply each digit by the value of its place and write the results as a sum. Each place is worth ten times the place to its right: ones, tens, hundreds, thousands and so on to the left of the decimal point, and tenths, hundredths and thousandths to its right.
Worked example: 30,527.08.
3 is in the ten thousands place, so it is worth 3 × 10,000 = 30,000. 0 is in the thousands place. It is worth 0 and is left out. 5 is in the hundreds place: 500. 2 is in the tens place: 20. 7 is in the ones place: 7. 0 is in the tenths place, and is left out. 8 is in the hundredths place: 8 × 0.01 = 0.08.
So 30,527.08 = 30,000 + 500 + 20 + 7 + 0.08.
The same sum is written three ways, and the names vary between textbooks. Expanded form adds the values: 30,000 + 500 + 20 + 7 + 0.08. Expanded notation shows each digit times its place value: (3 × 10,000) + (5 × 100) + (2 × 10) + (7 × 1) + (8 × 0.01). Exponential form writes the place values as powers of ten: (3 × 10⁴) + (5 × 10²) + (2 × 10¹) + (7 × 10⁰) + (8 × 10⁻²).
The powers count from the ones place, which is 10⁰ = 1. Each place to the left adds one to the power; each place after the decimal point takes one away, so tenths are 10⁻¹ = 1/10 and hundredths are 10⁻² = 1/100. Written with fractions, the 8 hundredths are 8 × 1/100.
Standard form is the number as normally written, 30,527.08, and adding the expanded form back up returns it.
Expanded Form Calculator FAQ
What is the expanded form of 4,825?
4,000 + 800 + 20 + 5. In expanded notation it is (4 × 1,000) + (8 × 100) + (2 × 10) + (5 × 1).
Are zeros written in expanded form?
No. A zero digit is worth 0, so it adds nothing to the sum: 7,006 = 7,000 + 6. The zeros still hold the 7 in the thousands place in the standard form, which is why 7,006 and 76 are different numbers.
What is place value?
The value a digit has because of where it stands. In 30,527.08 the 2 is in the tens place, so its place value is 20; the same digit in the hundreds place would be worth 200. A place value calculator lists every digit this way.
How do I write a decimal in expanded form?
The same way, using tenths, hundredths and thousandths for the places after the point. 0.375 = 0.3 + 0.07 + 0.005, or (3 × 1/10) + (7 × 1/100) + (5 × 1/1,000) with fractions.