Fraction to decimal calculator
This fraction to decimal calculator divides the numerator by the denominator and shows the exact result — including the digits that repeat forever when the division never ends, like 1/3 becoming zero point three recurring. Type any fraction below to see its own division worked out.
- Set up the division1 ÷ 3
- Divide — the remainder starts repeating1 ÷ 3 = 0.(3)
- Mark the repeating block0.(3)
How to convert a fraction to a decimal
Dividing the numerator by the denominator is the whole method — there's no second step.
- Set up the division: numerator ÷ denominator. For
1/3, that's1 ÷ 3. - Divide. If the remainder reaches 0, the decimal terminates there — done.
- If the remainder instead starts repeating a value it already produced, the digits from that point on repeat forever. Mark them rather than writing an endless string of digits.
Worked examples
A single repeating digit
1 ÷ 3 never reaches a remainder of zero — every step leaves aremainder of 1 again, so the digit 3 repeats forever: zero point three recurring.
A six-digit repeating block
1 ÷ 7 takes six steps before the remainder repeats one it already saw, so the whole six-digit block 142857 repeats: zero point one four two eight five seven recurring. Longer than 1/3's single digit, but the same rule — the block repeats because the remainder eventually does.
A terminating decimal
8's only prime factor is 2, so 3 ÷ 8 reaches a remainder of zero and stops: 0.375. No repeating block, because the division genuinely finishes.
Common values
Click a fraction to load it into the calculator above.
| Fraction | Decimal |
|---|---|
| 0.5 | |
| 0.25 | |
| 0.125 | |
| 0.2 | |
| 0.375 | |
| zero point three recurring | |
| zero point six recurring | |
| zero point one six recurring |
Where people get it wrong
1 ÷ 3 genuinely never ends. Writing it as 0.33 and then using that rounded figure in a further calculation carries the rounding error forward — the earlier the round, the larger the final error grows. The fix is to round once, at the very end, not partway through: zero point three recurring is exact; 0.33 already isn't.
Related calculators
Frequently asked questions
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. That's the entire method — a fraction is already a division written with a line instead of a ÷ sign.
Why does 1/3 never end?
Dividing 1 by 3 never reaches a remainder of zero — the remainder cycles through the same value forever, so the digit it produces repeats forever too. No amount of extra precision changes that; it is a property of the fraction, not a limitation of the calculator.
How can you tell if a fraction will terminate before dividing it?
Simplify the fraction, then look at the denominator. If its only prime factors are 2 and 5, the decimal terminates. Any other prime factor — most commonly 3 or 7 — forces a repeating decimal.
What does the line over the digits mean?
It marks the digits that repeat forever, the standard way to write a repeating decimal exactly instead of trailing off with dots and hoping the pattern is clear.
Is 0.333... the same as 1/3?
As shorthand, yes — but literally, no amount of finite 3s written out equals 1/3 exactly. The repeating-digit notation is the only way to write the exact value in decimal form; the calculator shows both.