Decimal to Fraction Converter - Terminating & Repeating

How to use this tool

Type your decimal into the input field.
For repeating decimals, wrap the repeating digits in parentheses, e.g. 0.(3).
The tool instantly shows the simplified fraction, numerator, denominator, and a mixed-number form when the result is improper.
Use the example buttons to try common values like 0.75 or 0.(3).

How to convert a decimal to a fraction

Every terminating decimal can be written as an exact fraction by multiplying by the appropriate power of 10. For example, 0.75 becomes 75/100, which simplifies to 3/4 after dividing by GCD(75, 100) = 25.

The converter builds that numerator and denominator from the digits you enter using BigInt integer arithmetic, then reduces them with an exact GCD. That means a large whole part is not rounded through a floating-point value before conversion: for example, 9007199254740993.1 becomes 90071992547409931/10. The decimal preview is only for convenience and may be unavailable for values outside the finite Number range. To keep the browser calculation predictable, inputs permit up to 1,000 whole-part digits and 10 decimal or repeating digits.

Terminating vs. repeating decimals

A terminating decimal ends after a finite number of digits (0.5, 0.125, 3.14). A repeating decimal has one or more digits that repeat forever (0.333… = 0.(3), 0.1666… = 0.1(6)). Both types represent rational numbers and can be expressed as exact fractions.

Repeating decimal notation

Enter repeating digits inside parentheses. Examples:

0.(3) -> 0.333… -> 1/3
0.(6) -> 0.666… -> 2/3
0.1(6) -> 0.1666… -> 1/6
0.(142857) -> 0.142857142857… -> 1/7
0.(9) -> 0.999… -> 1 (a well-known mathematical identity)

Mixed numbers

An improper fraction whose absolute value is greater than 1 can also be written as a mixed number. For example, 7/4 = 1 3/4. The calculator shows both forms for improper results; a proper fraction such as 3/4 remains in fraction form.

Common decimal-to-fraction conversions

0.5 = 1/2
0.25 = 1/4
0.75 = 3/4
0.2 = 1/5
0.125 = 1/8
0.(3) = 1/3
0.(6) = 2/3

Frequently asked questions

How do I convert 0.75 to a fraction?

0.75 has two decimal places. Multiply by 100 to get 75/100, then simplify by dividing by GCD(75,100) = 25: 75/100 = 3/4.

How do I convert a repeating decimal like 0.333… to a fraction?

Enter 0.(3) in the calculator. Algebraically: let x = 0.333…, then 10x = 3.333…, subtract x: 9x = 3, so x = 3/9 = 1/3.

What notation do I use for repeating decimals?

Enclose the repeating digit(s) in parentheses. Examples: 0.(3) for 0.333…, 0.(142857) for 0.142857142857…, 0.1(6) for 0.1666…

What is a mixed number?

A mixed number combines a whole number and a proper fraction, e.g. 1 1/2 instead of 3/2. The calculator shows a mixed form when the absolute value of the result is greater than 1.

Can the converter preserve very large whole numbers?

Yes. Fraction construction, reduction, mixed-number formatting, and displayed numerator and denominator use exact BigInt integers, so accepted digits are never first rounded to a JavaScript Number. The decimal preview is only an approximation and is marked unavailable when it would be outside Number’s finite range. Inputs allow up to 1,000 whole-part digits and 10 digits after the decimal or in the repeating section.