Fraction to Decimal Calculator
Convert any fraction n/d to its decimal form, including detection of repeating decimals.
Result
1/3
0.(3)
Repeating block has 1 digit.
- Decimal (truncated)0.3
- Repeats?Yes — repeats from position 1
- Whole part0
Step-by-step
- Long-divide 1 by 3: whole part = 0, remainder = 1.
- Continue dividing the remainder × 10 by the denominator until remainder repeats or reaches 0.
- A remainder repeated → repeating decimal: 0.(3).
How to use this calculator
- Enter the numerator and denominator.
- Read the decimal — terminating or repeating.
- Hover the steps for the long-division process.
About this calculator
Every fraction has a decimal form that either terminates or repeats. The denominator (in lowest terms) determines which: if its only prime factors are 2 and 5, the decimal terminates; otherwise it repeats. This calculator does long division and tracks remainders to detect the repeat cycle, then displays it with parentheses.
Frequently asked
Because base 10 only "terminates" for fractions whose simplified denominator has prime factors of just 2 and/or 5. Anything else (3, 7, 11, …) creates a remainder cycle.
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