1/6 as a Decimal

Repeating decimal, period 1 · 16.67% · simplified 1/6

1/6 = 0.16666666666666666 (repeating). The digits never stop, so the exact value is normally written with a repeating bar over the 1-digit block, and any written decimal is an approximation of it. As a percentage that is 16.67%.

Long division, step by step

Divide the numerator by the denominator the way it is done on paper: bring down a zero, note how many times the denominator fits, keep the remainder, repeat. The remainders are what decide whether the decimal stops.

The remainder repeats, so the digits must repeat with it — that is the whole mechanism behind a recurring decimal, not a quirk of the calculator.

Rounded to different precisions

How many places you keep depends on the use: money stops at two, engineering often wants three or four, and a science problem usually wants significant figures rather than decimal places.

Will it terminate?

A fraction has a terminating decimal exactly when its simplified denominator is built only from 2s and 5s. Here the denominator reduces to 6, which carries a prime factor other than 2 or 5, so the decimal recurs with a period of 1. This is a property of the denominator alone: the numerator never decides it.

Questions about 1/6

What is 1/6 as a decimal?

It does not terminate. The decimal begins 0.1666666666 with a repeating block of 1 digit, because the reduced denominator 6 contains a prime factor other than 2 or 5.

Is 1/6 already in simplest form?

Yes. 1 and 6 share no common factor, so the fraction cannot be reduced further and the decimal is generated from these exact digits.

How do I round 1/6 to two decimal places?

Two places give 0.17. The third digit decides it — when it is 5 or more the second digit rounds up, otherwise it stays.

What is 1/6 as a percentage?

16.67%, obtained by multiplying the decimal by 100. It is the same number with the decimal point moved two places to the right, and the same rounding rules apply.