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Decimal to Fraction Converter

Turn a finite or repeating decimal into a reduced fraction using integer arithmetic, with readable working steps.

Browser-based · No signup · Transparent assumptions

Open converter Free to use · No signup
  1. 01Enter your values
  2. 02Adjust your settings
  3. 03Review your results
All 23 utilities
Input mode
Decimal value
Enter a decimal
Supports 0.75, -2.5, 0.333..., 0.1(6). Trailing ... means the last digit repeats. Parentheses mark the repeating block.
Export
½

Enter a decimal to begin

Your fraction, mixed number, percentage, and step-by-step working will appear here.

This changes the approximate card only; the exact BigInt fraction stays unchanged. Limit each decimal field to 100 characters.

Calculations run in this browser. Shared URLs can contain input values. Review links before sharing financial, dietary or birth-date information.

When to use this calculator

Turn a measurement or repeating-decimal exercise into a simplified fraction. Enter the repeating block explicitly with parentheses and use the exact result when a floating-point approximation would hide the intended value.

Review the worked example and assumptions below, then use the supported report or copy controls to keep the result with its inputs. Calculations run in this browser; a shared URL can include the values you entered.

How to use Decimal to Fraction Converter

  1. Enter a decimal such as 0.75 or 0.(3), or choose the repeating-digit fields.
  2. Review the exact reduced fraction, mixed number and conversion steps.
  3. Copy the result or download a text report; use simple approximations only when appropriate.

Exact decimal conversion

A terminating decimal with n digits after the point is an integer divided by 10^n. A repeating block of r digits introduces a denominator factor of 10^r minus 1. Greatest-common-divisor reduction gives the simplest exact fraction. Approximation cards are separate from the exact fraction.

Worked example

0.75 = 75/100 = 3/4
0.(3) = 3/9 = 1/3
0.1(6) = (16 - 1)/90 = 1/6

Assumptions and limits

Up to 100 digits per field. Exact fraction arithmetic uses BigInt; decimal previews and approximation cards use floating-point numbers. Trailing dots repeat the last digit; use parentheses to make the repeating block explicit. Scientific notation is not accepted.

Reference: MDN: BigInt integer arithmetic. Model/source review: 19 October 2026. See the tool-specific scope and precision limits above.

Frequently asked questions

Is 0.333 the same as one third?

No. 0.333 is exactly 333/1000. Enter 0.(3) for one third.

Can I enter negative decimals?

Yes. Put a minus sign before the whole number.

Are approximation cards exact?

Only the exact fraction panel represents the supplied decimal precisely. A simpler denominator may introduce an error.

State a repeating block explicitly

Choose the intended finite or repeating notation before converting. Inspect the exact fraction separately from its approximate decimal preview.

Scope of this workflow

A finite string such as 0.333 differs from a repeating block. Exact arithmetic and floating-point approximation cards have distinct roles; scientific notation is outside this input format.

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