Fraction to Decimal Converter
Convert a fraction to a decimal. Enter a numerator and denominator (negatives are fine) to get the exact decimal, with any repeating block shown in parentheses and described in bar notation.
Example: with Numerator -2 · Denominator 9 → Decimal: -0.2222222222….
- Exact form-0.(2) — the block 2 repeats forever (overbar: 2̅)
- Rounded (6 dp)-0.222222
- As a percent-22.2222%
Computed by the calculator below using its default values. Change any input to see your own numbers.
The decimal is numerator ÷ denominator. When a remainder repeats during long division, the digits repeat too, giving a recurring decimal marked here with parentheses.
What long division reveals
Dividing the top of a fraction by the bottom either stops or falls into a loop. It stops when a remainder hits zero — that is a terminating decimal like 0.125. It loops when a remainder repeats, because from that point on the digits must repeat too, giving a recurring decimal like 0.3333.
The denominator decides which happens. Reduce the fraction, then look at the bottom: if its only prime factors are 2 and 5, the decimal terminates, since 2s and 5s divide evenly into powers of ten. Any other factor — a 3, a 7, an 11 — forces a repeating block, which we mark with parentheses here and with an overbar (vinculum) in textbooks.
How it’s calculated
The decimal is numerator ÷ denominator by long division. Tracking remainders shows whether it terminates or repeats: a repeated remainder begins the recurring block, shown here in parentheses and by an overbar in textbooks. A reduced fraction terminates only when the denominator factors into 2s and 5s.
Exact repeating detection assumes whole-number inputs. A decimal entered directly is shown as a rounded approximation instead.
Fractions as decimals
| Fraction | Decimal | Type |
|---|---|---|
| 1/2 | 0.5 | terminating |
| 1/4 | 0.25 | terminating |
| 1/8 | 0.125 | terminating |
| -2/9 | -0.(2) = -0.222… | repeating |
| 1/3 | 0.(3) = 0.333… | repeating |
| 1/7 | 0.(142857)… | repeating, 6-digit block |
Computed by long division; a reduced fraction terminates only when the denominator has just 2s and 5s as prime factors.
Common mistakes
- Rounding too early — 2/3 is 0.6667 only as an approximation; the exact value is 0.6 repeating.
- Marking every long decimal as repeating; 1/8 = 0.125 terminates cleanly.
- Dropping the sign — a negative numerator or denominator makes the whole decimal negative.
Frequently asked questions
What is -2/9 as a decimal?
−0.2222, written −0.(2) or with a bar over the 2. The digit 2 repeats forever.
How do I turn a fraction into a decimal?
Divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75. If the division never ends, the result is a repeating decimal.
Which fractions give repeating decimals?
A fraction in lowest terms terminates only if its denominator has no prime factors other than 2 and 5. Otherwise it repeats, like 1/3 or 1/7.
What do the bar and parentheses mean?
They mark the repeating block. 0.(3) and 0.3 with an overbar both mean 0.3333 forever; 0.1(6) means 0.16666.