Decimal to Fraction

Turn any decimal into a simplified fraction — including repeating decimals — free, instant and private. The conversion runs entirely in your browser and nothing is uploaded.

Use parentheses to mark repeating digits, for example 0.(3) = 0.333…, 1.16(6), or 0.8(3).

How to use the decimal to fraction converter

  1. Type a decimal. Enter a value such as 0.75, -1.5 or 2.125 in the box above.
  2. Mark any repeat. For a repeating decimal, use parentheses like 0.(3), or tick the checkbox and say how many trailing digits repeat.
  3. Read the fraction. The simplified fraction, mixed number, exact decimal and percentage appear instantly, with the working steps shown below.

About this tool

This free decimal-to-fraction converter finds the exact fraction behind any decimal and reduces it to lowest terms. For terminating decimals it writes the number over the right power of ten and divides out the greatest common divisor. For repeating decimals it uses the standard algebraic method, so 0.(3) becomes 1/3 and 0.8(3) becomes 5/6 — exactly, with no rounding. All arithmetic uses whole-number (BigInt) math, so even long decimals convert precisely.

Alongside the simplified fraction you get the mixed-number form, the exact decimal expansion written back with its repeating block, and the equivalent percentage. Everything is computed locally in your browser, so your numbers are never uploaded and the tool keeps working offline once the page has loaded.

Frequently asked questions

How do I enter a repeating decimal?

Wrap the repeating digits in parentheses. For 0.333… type 0.(3); for 1.2454545… type 1.2(45); for 0.8333… type 0.8(3). If you prefer, tick the “last digits repeat” box and enter how many of the digits you typed should repeat.

How is a repeating decimal turned into a fraction?

By algebra: let x equal the decimal, multiply by powers of ten so one full repeating block lines up on both sides, then subtract to cancel the endless tail. That leaves a whole-number fraction, which is then reduced. The steps box shows the exact numbers used.

Why does 0.(9) become 1?

Because 0.999… genuinely equals 1. Using the repeating-decimal method, x = 0.999…, 10x = 9.999…, so 9x = 9 and x = 1. It is a well-known result, not a rounding error, and the tool reports it faithfully.

Is the result always in lowest terms?

Yes. After building the raw fraction the tool divides the numerator and denominator by their greatest common divisor, so the fraction you see cannot be simplified any further.