1
Enter the fraction
Provide integer numerator and denominator values; the denominator cannot be zero.
Math
Free tool
Fraction to Decimal Calculator
Convert an integer fraction to a decimal, reduce it, and identify whether its decimal expansion terminates.
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Convert a fraction to a decimal
Enter integer numerator and denominator values. Negative fractions are supported; the denominator cannot be zero.
Result
How to use this calculator
Three steps to an answer you can interpret.
2
Divide and simplify
The tool reduces the fraction before classifying its decimal form.
3
Check exactness
Terminating decimals are exact; repeating decimals are shown as approximations.
Understand the result
Divide the numerator by the denominator. The calculator also reduces the fraction first so it can classify the decimal expansion exactly.
Division formula
Decimal = numerator ÷ denominator. A denominator of zero is undefined and is rejected.
Worked examples
1/4 equals 0.25. The fraction 1/3 produces approximately 0.333333333333 when shown to 12 decimal places.
The reduced denominator determines whether the decimal terminates.
Terminating decimals
A reduced fraction terminates in base 10 when its denominator has no prime factors other than 2 and 5.
Non-terminating decimals
If another prime factor remains in the reduced denominator, the decimal expansion does not terminate. The calculator clearly labels the displayed decimal as an approximation.
Why some fractions repeat
Base 10 is built from the prime factors 2 and 5. Denominators containing other prime factors cannot be represented with a finite number of decimal places.
Reduced fractions
Reducing before classification matters. For example, 2/4 reduces to 1/2, whose denominator contains only the factor 2, so its decimal terminates.
Common mistakes
- Dividing the denominator by the numerator instead of the other way around.
- Using zero as the denominator.
- Treating a rounded repeating decimal as exact.
More useful tools
View allFrequently asked questions
Are negative fractions supported?
Yes. Either input may carry the sign, provided the denominator is not zero.
Why is 1/3 labelled approximate?
Its decimal expansion continues indefinitely, so the UI shows a finite approximation rather than pretending it is exact.