Fraction to Decimal Converter
Convert fractions to decimals (with repeating-cycle detection and step-by-step long division), convert decimals back to fractions (including 0.(3) and 0.333... repeating notation), and add, subtract, multiply, or divide two fractions.
Input
Leave blank for a simple fraction; set it to enter a mixed number (e.g. 2 3/4).
Output
| Property | Value |
|---|---|
| No data yet | |
Guides
Convert a fraction to its decimal value, turn a decimal back into a fraction, or add, subtract, multiply, and divide two fractions — all in one tool. It detects repeating decimals, shows the exact repeating cycle, and walks through the long division step by step so you can see why a fraction terminates or repeats.
What it does
Pick a Mode and fill in the fields:
- Fraction → Decimal — enter a numerator and denominator (plus an optional whole number for mixed numbers like 2 3/4). You get the decimal value, the simplified fraction, the percentage, and, when the decimal repeats, its cycle length and repeating digits.
1/7becomes0.(142857)— the parentheses mark the block that repeats forever. - Decimal → Fraction — type a decimal and get the fraction back. Repeating decimals are supported in two notations: parentheses (
0.(3)) or an ellipsis (0.333...). An optional Max denominator caps how complex the fraction can get, returning the closest simple approximation instead of the exact value. - Fraction operations — add, subtract, multiply, or divide two fractions and see the simplified result, its mixed-number form, and its decimal value.
Every result also includes a step-by-step long division panel showing each remainder, the digit it produces, and exactly where a remainder repeats — the moment a decimal starts to cycle.
How to use it
- Choose a mode from the dropdown.
- Enter your numbers. Results update as you type.
- Copy the results table (as CSV) or the long-division steps with the buttons on each output.
Frequently asked questions
What does the notation like 0.(3) mean?
The digits inside the parentheses repeat endlessly. 0.(3) is 0.3333… (which equals 1/3), and 0.58(3) is 0.58333…. It's a compact, unambiguous way to write a repeating decimal.
How do you convert a repeating decimal back to a fraction?
For a purely repeating decimal, the repeating block goes over as many 9s as it has digits — 0.(3) = 3/9 = 1/3. When there are non-repeating digits after the point, the tool scales by the right power of ten first, then simplifies. You can enter the repeat with either parentheses or a trailing ellipsis.
Why do some fractions terminate and others repeat?
A fraction in lowest terms terminates only when its denominator's prime factors are just 2s and 5s (the factors of 10). Any other prime factor — like the 7 in 1/7 — forces the long division to cycle forever. The long-division panel makes this visible: it stops when a remainder reappears.
What is the "Max denominator" option for?
Real-world measurements often want a simple fraction rather than an exact one. Capping the denominator finds the closest fraction whose denominator stays within your limit, and the result is flagged as an approximation when it isn't exact.
Privacy
This tool runs entirely in your browser. Your numbers are never uploaded, logged, or sent to a server — the math happens locally on your device.