Fraction to Decimal Calculator — convert a fraction to a decimal

How it works

A fraction a/b is really a division waiting to happen: the bar between numerator and denominator means "divide". So converting a fraction to a decimal is simply carrying out that division:

decimal = numerator ÷ denominator

For 3/4, that's 3 ÷ 4 = 0.75. The numerator is how many parts you have, the denominator how many equal parts make a whole, and the decimal expresses that same amount in tenths, hundredths and so on.

Whether the decimal terminates (stops) or repeats depends on the denominator once the fraction is in lowest terms: if its only prime factors are 2s and 5s, the decimal ends; any other factor (like 3 or 7) makes it repeat forever. That's why 3/4 and 7/8 stop but 1/3 and 1/7 go on.

Worked example

Convert 3/4 to a decimal:

3 ÷ 4 = 0.75

More examples: 7/8 = 7 ÷ 8 = 0.875 (it terminates, since 8 = 2³); 1/3 = 1 ÷ 3 = 0.333... (it repeats, since 3 isn't a factor of 10); and an improper fraction like 9/4 = 9 ÷ 4 = 2.25, greater than 1 because the numerator exceeds the denominator.

Frequently asked questions

How do I convert a fraction to a decimal?

Divide the top number by the bottom number. For 5/8, compute 5 ÷ 8 = 0.625. If the division doesn't come out evenly, keep going to as many decimal places as you need — or recognise a repeating pattern and mark it.

Why do some fractions repeat and others don't?

It comes down to the denominator's prime factors once the fraction is fully reduced. Powers of 2 and 5 divide evenly into powers of 10, so those give terminating decimals (1/8 = 0.125). Any other prime factor — 3, 7, 11 and so on — can't, so the long division never resolves and a block of digits repeats forever (1/3 = 0.333..., 1/7 = 0.142857...).

How do I write a repeating decimal exactly?

Put a bar (or dots) over the repeating block: 1/3 = 0.3̄ and 1/7 = 0.142857 with the whole six-digit block repeating. This calculator shows the first several decimal places, which is enough to recognise the pattern; the bar notation captures it exactly in writing.

What about improper fractions and mixed numbers?

An improper fraction (numerator larger than denominator) just gives a decimal greater than 1 — 9/4 = 2.25. For a mixed number like 2¾, convert the fraction part and add the whole number: ¾ = 0.75, so 2¾ = 2.75. Or turn it into the improper fraction 11/4 first and divide.

How do I turn the decimal into a percentage?

Multiply by 100 and add a percent sign. Since 3/4 = 0.75, that's 75%. Fractions, decimals and percentages are three ways of writing the same value, and you move between them by dividing (to a decimal) and scaling by 100 (to a percent).

Can the denominator be zero?

No — a fraction with a zero denominator is undefined, because dividing by zero has no meaning. Every other whole-number denominator is fine, including negatives, which simply make the decimal negative (−3/4 = −0.75).