Question

Is 4.`bar4` rational or irrational?

Answer 1

It is a rational number. See explanation.

Explanation:

A repeating decimal is always a rational number. To write it as a fraction you can do the following:

`x=4.44...`

`10x=44.44...`

`10x=40+x`

`9x=40`

`x=40/9=4 4/9`

A number is rational if it can be written as a fraction (improper fraction or a mixed number is also a fraction). Here we wrote number `x` as a fraction, so it is a rational number.