Converts a fraction into a decimal and a decimal back into a fraction, simplified, with the percentage alongside. Recurring decimals are written exactly rather than cut off after a handful of digits.
Key terms
- Numerator — the top number, how many parts you have.
- Denominator — the bottom number, how many parts make a whole. It can never be zero.
- Simplified — top and bottom divided by their greatest common divisor, so 6/8 becomes 3/4. The same number, written smaller.
- Recurring — a decimal whose digits repeat for ever, like 1/3 = 0.333…
How it works
Both directions
decimal = numerator ÷ denominator · fraction = digits ÷ 10places, then ÷ GCD
0.125 has three decimal places, so it starts as 125/1000; dividing both by 125 gives 1/8.
Recurring decimals are written exactly
5/6 is not 0.8333333. It is 0.8 followed by a 3 that never stops, and printing ten 3s then stopping states something false about a number that has an exact form.
So the conversion does real long division and remembers every remainder along the way. When a remainder turns up a second time, the digits produced since then must repeat for ever — that block is the recurring part, and it is shown in brackets: 0.8(3). It is why 1/7 comes out as 0.(142857), a six-digit cycle, rather than a row of digits that looks arbitrary.
0.333 is not one third
Going the other way, the calculator converts the number you actually typed. 0.333 is exactly 333/1000. It is not quietly upgraded to 1/3, because those are different numbers — 1/3 is 0.333… going on for ever, and the gap between them is real.
This is why a long decimal copied from elsewhere can produce a large, ugly fraction. That is the arithmetic being honest about a number that was already rounded before you pasted it.
How to use this calculator
- Choose which direction you are converting.
- Enter the fraction’s top and bottom, or the decimal.
- Read the exact form first — brackets mean those digits repeat for ever.
- The rounded value and the percentage are there for when an exact answer is not what you need.
Frequently asked questions
Why can the denominator not be zero?
Because dividing by zero is not defined — there is no number that answers “how many nothings make one”. The calculator declines rather than showing infinity.
What do the brackets in the answer mean?
The digits inside them repeat for ever. 0.8(3) means 0.8333… and 0.(142857) means 142857142857… repeating without end. It is a standard notation and it is exact.
Which fractions give a recurring decimal?
A fraction terminates only when its simplified denominator has no prime factors other than 2 and 5 — the factors of ten. That is why halves, quarters, fifths and eighths stop neatly, while thirds, sixths and sevenths do not.
How do I turn a recurring decimal back into a fraction?
Not by typing it in — this converter uses the digits you enter, so it treats 0.333 as 333/1000. The algebraic method is to multiply by a power of ten and subtract: for 0.333…, 10x − x = 3, so x = 3/9 = 1/3.
Is 0.999… equal to 1?
Yes, exactly — not nearly. The same subtraction gives 9x = 9, so x = 1. They are two ways of writing the same number, which surprises most people the first time.
