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 the mixed form whenever the fraction 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.

Decimal to Fraction Converter - Terminating & Repeating

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

When a fraction is greater than 1, it can also be written as a mixed number. For example, 7/4 = 1 3/4. The calculator shows both forms.

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