Convert any fraction into a decimal, or turn a decimal into its simplest fraction.

Converting between fractions and decimals

Fractions and decimals are two ways of writing the same quantity, and moving between them is a routine task in cooking, construction, and schoolwork. Dividing the numerator by the denominator turns any fraction into a decimal.

Going the other way is slightly subtler. A terminating decimal like 0.625 converts exactly, because it can be written over a power of ten and then reduced, in this case to five eighths. Repeating decimals cannot be written exactly this way, so they are approximated to the nearest simple fraction.

The reduction step matters for clarity. Writing five eighths is far more useful than 625 over 1000, even though both are correct, which is why this tool always simplifies the result.

The formula

Worked example

3/4 = 3 / 4 = 0.75. And 0.625 = 625/1000, reduced to 5/8.

How to read your result

Terminating decimals always convert to an exact fraction. Repeating decimals are approximated to the nearest simple fraction here.

Frequently asked questions

How is the fraction simplified?

By dividing the numerator and denominator by their greatest common divisor.

What about repeating decimals?

They are rounded, so the fraction is a close approximation rather than exact.

Can it handle improper fractions?

Yes - 7/4 returns 1.75 just fine.

Related calculators

Percentage CalculatorRatio CalculatorAverage CalculatorPercentage Increase CalculatorPercentage Decrease Calculator

Roxish — free, formula-transparent calculators for school, work, and everyday decisions.