Fraction to Decimal Calculator
Convert any fraction to a decimal and percentage. Detects repeating decimals and shows the recurring pattern, e.g. 1/6 = 0.1(6) = 16.67%.
About the Fraction to Decimal Calculator
This fraction to decimal calculator divides any numerator by any denominator and shows the exact decimal form — including detection of repeating decimals. Instead of an abruptly rounded 0.16666667, it tells you that 1/6 = 0.1(6), where the digit in parentheses repeats forever (the same thing textbooks write with an overline). You also get the value as a percentage.
The tool performs true long division and tracks remainders: the moment a remainder repeats, the decimal digits must cycle, so the calculator knows the exact repeating block. A fraction terminates only when its simplified denominator has no prime factors other than 2 and 5 — that is why 3/8 = 0.375 ends, but 1/3, 1/6 and 5/7 all repeat.
Students checking homework, teachers building worksheets, and anyone converting odds, ratios or measurements to decimals or percentages will find it faster and more precise than a basic calculator.
How to Use the Fraction to Decimal Calculator
- 1Enter the numerator (top number) of the fraction.
- 2Enter the denominator (bottom number) — any non-zero whole number.
- 3Read the decimal, with any repeating block shown in parentheses.
- 4Check the percentage value and whether the decimal terminates or repeats.
Frequently Asked Questions
What is 1/6 as a decimal?
1/6 = 0.1666... where the 6 repeats forever. This calculator writes it as 0.1(6) — the parentheses mark the repeating block, equivalent to the overline notation used in textbooks. As a percentage it is 16.6667% (rounded).
How do I know if a fraction gives a terminating or repeating decimal?
Simplify the fraction, then look at the denominator's prime factors. If they are only 2s and 5s, the decimal terminates (7/40 = 0.175 because 40 = 2³×5). Any other prime factor forces a repeat: 1/3, 1/7 and 5/12 all repeat. The calculator labels each result as terminating or repeating.
How do I convert a fraction to a percentage?
Divide and multiply by 100. For 3/8: 3 ÷ 8 = 0.375, so 3/8 = 37.5%. The calculator shows the percentage automatically — useful for marks, discounts and statistics.
What does 0.1(6) or the overline notation mean?
It marks digits that recur without end. 0.1(6) means 0.1666..., and 0.(142857) means 0.142857142857... — the whole 6-digit block of 1/7 repeats. Writing the exact repeating form avoids the rounding errors you get from truncating at 8 or 10 digits.
Does the calculator work with improper fractions and negatives?
Yes. 22/7 gives 3.(142857) — the classic π approximation — and -5/4 gives -1.25. Enter any whole-number numerator and any non-zero whole-number denominator, positive or negative.