Expanded Form Calculator
Break a number into place-value parts. Enter any number to see expanded notation or factors/exponents forms with clear steps instantly.
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Helping Notes
Numbers form uses place values (e.g., 4000 + 300 + 20 + 5). Factors show digit × place value. Exponents use 10k powers.
For decimals, place values continue after the point (tenths, hundredths, thousandths, …). Minus sign applies to the entire expansion.
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Term-by-Term Breakdown
What Is an Expanded Form Calculator?
An Expanded Form Calculator rewrites numbers and expressions as sums of simpler parts that reveal structure. For integers and decimals, it expresses a quantity via place values, e.g., thousands, ones, tenths, thousandths. For algebraic expressions, it distributes products and powers into a sum of terms (standard polynomial form). The tool accepts whole numbers, decimals, scientific notation, and symbolic inputs, then shows step‑by‑step transformations with clean, typeset formulas so learners can trace how each digit or factor contributes to the final value.
About the Expanded Form Calculator
Place‑value expansion follows base‑10 powers. If a number has digits , the calculator uses . Scientific notation expands further by distributing across the mantissa’s digits. For algebra, the engine applies the distributive law and, when helpful, the binomial theorem: . Throughout, exact forms (fractions, radicals) are preserved; decimal approximations are provided only on request. Results include intermediate steps, final expanded form, and optional simplification to collect like terms.
Place‑value (base 10):
Distributive law: General:
Binomial power:
How to Use This Expanded Form Calculator
- Choose Number or Algebra. Enter the integer/decimal (or expression) exactly as written.
- For numbers, select whether to show zeros explicitly (e.g., include terms whose coefficients are zero) and whether to display scientific notation steps.
- For algebra, choose distribute, expand powers, and combine‑like‑terms options to see intermediate lines or only the final expansion.
- Compute to view stepwise reasoning and a final expanded form that you can copy into assignments or reports.
Examples
- Integer place values: .
- Decimal place values: .
- With scientific notation: .
- Distribution: ; .
- Polynomial scaling: .
- Binomial power: .
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FAQs
What does expanded form mean for numbers?
It writes a number as a sum of each digit times its place value, revealing the contribution of thousands, ones, tenths, etc.
Can I include zero‑coefficient terms?
Yes. Showing zero terms emphasizes place positions; you can toggle them on or off.
How is expanded form different from standard form?
Expanded form is a sum of terms; standard form compresses those into a single numeral or a simplified polynomial.
Does the calculator handle decimals and scientific notation?
Yes. It expands decimals using negative powers of ten and can show intermediate steps from scientific notation.
Can I expand algebraic expressions like (x+3)(x−2)?
Absolutely—the tool distributes, applies binomial identities, and collects like terms to present a final polynomial.