Question

How do you write 1/6 as a decimal?

Answer 1

1/6 is 0.166666666666666666666. And it is 16.666666666666%

Explanation:

`1/6 = 0.1666666666666666666666666666666`

In percentage form:

`100times0.16666666666666666666666666666 = 16.66666666666666666666666666%`

Answer 2

`0.1dot6`

Explanation:

`1/6 = 0.1666666666....`

This is an infinite decimal because the string of 6's repeat indefinitely.

For practical purposes this is often rounded off - E.g. `0.167` but it is important to note that this is only an approximation of `1/6`.

To overcome this, we can use the dot or bar notation to indicate that a decimal digit (dot) or sequence of decimal digits (bar) repeat indefinitely.

Thus, in this case, as the `6` recurs indefinitely we can notate its first occurrence as `dot6`

Hence, `1/6 = 0.1dot6`

[NB: It is worth noting that repeating decimals should not be confused with irrational numbers. In fact, it can be shown that all repeating decimals are rational (like `1/6`). Whereas, irrational numbers have infinite decimals that do not repeat.]