Expanded Form Calculator

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Expanded form writes a number as the sum of each digit’s value. 4,382 = 4,000 + 300 + 80 + 2, or 4 × 1,000 + 3 × 100 + 8 × 10 + 2 × 1, or 4 × 10³ + 3 × 10² + 8 × 10¹ + 2 × 10⁰. Decimals work too: 56.073 = 50 + 6 + 0.07 + 0.003.

FreeStep by stepDecimals too

Number

Whole numbers up to 15 digits and up to 8 decimal places.

Try:

Expanded form

4,000 + 300 + 80 + 2

In words: four thousand three hundred eighty-two.

Exponential form	\(4 \times 10^{3} + 3 \times 10^{2} + 8 \times 10^{1} + 2 \times 10^{0}\)
Multiplication form	4 × 1,000 + 3 × 100 + 8 × 10 + 2 × 1
4 in the thousands place	4,000
3 in the hundreds place	300
8 in the tens place	80
2 in the ones place	2
Word form	four thousand three hundred eighty-two

Show steps

Write each nonzero digit times its place value, then add.
Multiplication form: 4 × 1,000 + 3 × 100 + 8 × 10 + 2 × 1

How to use the expanded form calculator

Type a whole number or a decimal; commas are optional.
Press Expand to see the standard expanded form, multiplication form, exponential form, word form and a place-value table.

Three ways to write expanded form

Standard: 3,507 = 3,000 + 500 + 7
Multiplication: 3 × 1,000 + 5 × 100 + 7 × 1
Exponential: 3 × 10³ + 5 × 10² + 7 × 10⁰

Zeros are skipped because 0 × 10 = 0.

Decimals in expanded form

Digits after the decimal point are tenths, hundredths, thousandths and so on: 2.46 = 2 + 0.4 + 0.06 = 2 × 1 + 4 × \(\frac{1}{10}\) + 6 × \(\frac{1}{100}\) = 2 × 10⁰ + 4 × 10⁻¹ + 6 × 10⁻².

Place value chart

Place	Value	Power of 10
Thousands	1,000	10³
Hundreds	100	10²
Tens	10	10¹
Ones	1	10⁰
Tenths	0.1	10⁻¹
Hundredths	0.01	10⁻²

Expanded form practice quiz: 10 questions

Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

What is expanded form?

Writing a number as the sum of the values of its digits, such as 352 = 300 + 50 + 2.

What is expanded form with exponents?

Each place value is written as a power of 10: 352 = 3 × 10² + 5 × 10¹ + 2 × 10⁰.

What happens to zeros?

Zero digits add nothing, so they are left out of the expanded form.

How do decimals work in expanded form?

Digits after the decimal point are tenths (10⁻¹), hundredths (10⁻²) and so on: 0.36 = 0.3 + 0.06.

What is the difference between standard form and expanded form?

Standard form is the usual way of writing a number (4,382); expanded form breaks it into place values.

Sources

OpenStax Prealgebra 2e: Introduction to Whole Numbers and Decimals

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Effortless Math Team

13 hours ago

Effortless Math Team

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