Fraction to Decimal Converter

Written byOleh Soloninupdated 5 October 2026

Direction

Numerator

Denominator

Result

Decimal0.625
Working5/8 = 625/1000 = 0.625
Repeating blocknone, the decimal terminates
Simplified fraction5/8
As a percentage62.5%

1/3 is 0.(3), not 0.333333

Divides numerator by denominator and gives the exact answer: a terminating decimal, or a recurring one with the period in brackets rather than a truncated tail.

A fraction is a division written down, so converting means dividing the top by the bottom. The interesting part is why some divisions stop and others never do.

The rule is short. If the simplified denominator contains only twos and fives, the decimal terminates. Any other prime factor — three, seven, eleven — produces a repeating block. That is why 1/8 is exact and 1/3 and 1/7 are not.

How to use

Choose the direction: from a fraction to a decimal, or from a decimal back to a fraction.
Enter the numerator and denominator, or type the decimal — a repeating part can be written in brackets.
Read the decimal, the simplified fraction, the period if there is one, and the step-by-step division.

Which fractions end and which repeat

A fraction terminates when the denominator of its simplified form contains nothing but twos and fives, because those are the prime factors of ten. That is why 5/8 gives an exact 0.625 and 7/16 gives 0.4375, while 1/3 becomes 0.(3) and never settles.

The length of the period is fixed by the denominator, not by the numerator. Sevenths always repeat six digits: 1/7 is 0.(142857) and 2/7 is 0.(285714) — the same six digits, started at a different point.

Worked out with this calculator; brackets mark the repeating block.
Fraction	Decimal	Period
5/8	0.625	terminates
3/4	0.75	terminates
7/16	0.4375	terminates
1/3	0.(3)	3
2/7	0.(285714)	285714

What this calculator shows

The exact decimal with the repeating block marked when there is one
The simplified fraction and an approximate value for calculations
The same quantity as a percentage

What to keep in mind

The period is found by long division, watching for a remainder to repeat, so even long ones show up: 1/7 repeats on 142857.
Very long periods are cut at forty digits, beyond which the notation stops being readable.

FAQs

Can I tell in advance whether it repeats?

Factor the denominator of the simplified fraction. Only twos and fives terminate — 8 gives 0.625 and 16 gives 0.4375. Any other prime brings a period: sevenths repeat six digits, as in 0.(142857).

What do the brackets mean?

The repeating group. 0.41(6) means 0.41666… forever. It is standard mathematical notation, not an abbreviation.

How long can a period be?

At most the denominator minus one. 1/7 repeats over six digits — 142857 — which is the maximum for seven. Such denominators are called full reptend primes.

How do I convert a repeating decimal back to a fraction?

A period of n digits sits over n nines: 0.(3) = 3/9 = 1/3, and 0.(27) = 27/99 = 3/11. Digits before the period add zeros after the nines.

What is 5/8 as a decimal?

0.625, and it terminates because the denominator is a power of two. By contrast 1/3 gives 0.(3), a repeating decimal that no finite string of digits can express exactly.

Worked example

Five eighths

Input: 5/8

Output: 0.625 — it terminates

Note: The denominator 8 is 2³, twos only, so no period appears. 5/12 gives 0.41(6) instead: twelve carries a factor of three.

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Result

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