Exact fraction calculator
Decimal to Fraction Calculator
Enter a terminating decimal or repeating notation such as 0.(3). Get the simplified fraction, mixed number, and exact steps immediately.
Reverse conversion
Fraction to decimal
Enter integers. Repeating digits appear in parentheses instead of being silently rounded.
How decimal-to-fraction conversion works
A terminating decimal uses place value. For 0.75, two decimal places give 75/100; dividing both parts by 25 gives 3/4.
A repeating decimal needs a different exact step. For 0.(3), subtracting the original value from ten times the value removes the repeating tail, which gives 3/9 = 1/3. This calculator performs the equivalent operation with whole integers.
Input rules and precision
Terminating decimals
Use ordinary notation such as 0.125, .5, or -12.375.
Repeating decimals
Wrap only the repeating block: 0.(3), 0.1(6), or 1.2(34).
No guessed ellipses
An entry such as 0.333... is rejected because the dots do not identify an exact repeating block.
Sources and method
The calculator uses place value and greatest-common-factor reduction, following the same rational-number method described in the references below.
- OpenStax — Rational NumbersExplains rational numbers and decimal representations.
- OpenStax — Multiply and Divide FractionsCovers equivalent fractions and simplifying with common factors.
Frequently asked questions
How do I convert a decimal to a fraction?
Write the decimal digits over a power of ten, then divide the numerator and denominator by their greatest common factor. For example, 0.75 becomes 75/100, then 3/4.
How do I enter a repeating decimal?
Put only the repeating block in parentheses. Enter 0.(3) for 0.333… or 1.2(34) for 1.2343434….
Can a repeating decimal be written as a fraction?
Yes. Every repeating decimal is rational and can be represented by an exact fraction. This calculator uses integer arithmetic to avoid floating-point approximation.
What is 1.25 as a fraction?
1.25 equals 125/100, which simplifies to 5/4 or the mixed number 1 1/4.
Why does the reverse result use parentheses?
Parentheses identify the repeating block. For example, 1/6 is shown as 0.1(6), meaning the 6 repeats indefinitely.