Fraction to Decimal Calculator

Convert any fraction to a decimal, and see whether it terminates or repeats — which depends entirely on the denominator.

As a decimal

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As a decimal—

Type of decimal—

Repeating part—

Whole part—

As a percentage—

How this was worked out

The rule

decimal = numerator ÷ denominator

Why it works

Dividing the numerator by the denominator gives the decimal. Whether the division ever ends is decided by the denominator alone: if its only prime factors are 2 and 5, the decimal terminates. Anything else repeats forever.

How to do it by hand

Divide the numerator by the denominator
Keep going while the remainder is not zero
If a remainder repeats, the digits from that point repeat forever
Multiply by 100 for the percentage

What is worth knowing

The rule about 2 and 5 is not arbitrary — they are the prime factors of ten, our base. In base 10, only fractions whose denominators divide a power of ten can terminate. That is why 1/3 repeats but 1/8 does not, and it is also why the same fraction behaves differently in another base: 1/3 terminates neatly in base 3. The repeating block can never be longer than one less than the denominator, because there are only that many possible remainders, and once a remainder repeats the whole pattern must.

Frequently asked questions

Why do some fractions repeat and others don't?

It depends on the denominator's prime factors. Only 2 and 5 allow a terminating decimal, because they are the factors of ten.

How long can the repeating part be?

At most one less than the denominator. There are only that many possible remainders, so the pattern has to repeat by then.

Is 0.999… equal to 1?

Yes, exactly. They are two ways of writing the same number, not two numbers that happen to be close.

Why does 1/3 repeat in decimal but not in base 3?

Because 3 divides a power of 3 but not a power of 10. Whether a fraction terminates depends on the base you write it in.