CALCULATE WITH CONFIDENCE

Number Fundamentals & Precision

Expanded Form Calculator

Write a finite decimal as its nonzero powers-of-ten terms.

Exact arithmetic

Decompose a number by place

Exact powers of ten
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Expanded form

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The subject in plain language

What is expanded form?

Expanded form writes a number as the sum of the value contributed by each nonzero digit. It reveals how place value builds the complete number.

It is useful for reading large or precise numbers, understanding decimal places, and checking that a written number has been interpreted correctly.

A zero may not produce a term, but its position still matters. In 304.052, the zeroes hold the places that make 3 mean three hundreds and 5 mean five hundredths.

Key idea

See the relationship

Quick guide

How to use this calculator

  1. Enter a finite decimal.
  2. Read the nonzero digit-by-place terms.
  3. Use the reconstruction check to confirm the original value.

Calculation method

Decompose by place

Each nonzero digit is multiplied by the power of ten belonging to its position. A negative sign applies to the complete magnitude.

Worked example

Expanded form of 304.052

Zero places do not add a term, but their positions remain represented by the surrounding exponents.

304.052 = 3×10² + 4×10⁰ + 5×10⁻² + 2×10⁻³

Supported inputs

Precision and limits

Readable expression

Use at most 60 digits.

Exact decimal input

Finite decimals use integer-scaled arithmetic, with no binary floating-point conversion.