Question

Is 3.333... an irrational number?

Answer 1

`3.33333............=10/3` It is rational because it can be written in the form `p/q`, therefore it is not irrational.

Explanation:

No, it not irrational as it is a rational number. In fact any decimal number which ends after a limited number of places beyond decimal point, or in which digits repeat endlessly after decimal place, are rational number.

Here in `3.33333............`, `3` gets repeated endlessly i.e. till infinity and hence is a rational number.

Let `x=3.33333............`, then `10x=33.3333............`.

Subtracting first from second, we get

`9x=30`, hence `x=30/9=10/3` or

`3.33333............=10/3`

This is seen to be a rational number `p/q`, so it is not irrational.