Enter any number — whole or decimal — into the Expanded Form Calculator and see it broken down by place value. Your number is shown in three formats: expanded notation (e.g. 5,000 + 300 + 20 + 5), expanded factor form (e.g. 5 × 1,000 + 3 × 100), and expanded exponential form (e.g. 5 × 10³ + 3 × 10²). A word form output is also included.
Expanded Number Form
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Expanded Factor Form
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Expanded Exponential Form
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Word Form
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Expanded form (also called expanded notation) is a way of writing a number to show the value of each individual digit based on its place value. For example, 5,325 in expanded form is 5,000 + 300 + 20 + 5. This helps you see the mathematical contribution of every digit in the number.
For decimals, you extend the place value system to the right of the decimal point: tenths (0.1), hundredths (0.01), thousandths (0.001), and so on. So 709.104 in expanded form is 700 + 9 + 0.1 + 0.004. In factor form, that becomes 7 × 100 + 9 × 1 + 1 × 0.1 + 4 × 0.001.
Expanded exponential form expresses each place value as a power of 10. For example, 5,325 becomes (5 × 10³) + (3 × 10²) + (2 × 10¹) + (5 × 10⁰). For decimal digits, negative exponents are used — the tenths place is 10⁻¹, hundredths is 10⁻², and so on.
Expanded number form simply adds the place values together: 5,000 + 300 + 20 + 5. Expanded factor form shows the multiplication behind each term: (5 × 1,000) + (3 × 100) + (2 × 10) + (5 × 1). Both represent the same value — they just show different levels of detail.
Yes. For a negative number like -5,325, the expanded form applies to the absolute value of the number and the negative sign is preserved: -(5,000 + 300 + 20 + 5) or written as -5,000 + (-300) + (-20) + (-5). This calculator supports negative numbers automatically.
Scientific notation expresses a number as a single digit (1–9) multiplied by a power of 10, e.g. 5.325 × 10³. Expanded form breaks a number into a sum of each digit's place value contribution. They both use powers of 10, but expanded form shows every digit's value separately while scientific notation compresses the whole number into one expression.
35,713 in expanded number form is 30,000 + 5,000 + 700 + 10 + 3. In expanded factor form: (3 × 10,000) + (5 × 1,000) + (7 × 100) + (1 × 10) + (3 × 1). In expanded exponential form: (3 × 10⁴) + (5 × 10³) + (7 × 10²) + (1 × 10¹) + (3 × 10⁰).
Expanded form builds a strong understanding of place value, which is foundational for arithmetic, algebra, and algorithms like partial products multiplication. It helps students and learners visualise exactly how large or small each digit's contribution is within a number, making mental math and estimation much easier.