An irrational number is a number that can not be expressed in a rational form, that is, as a fraction of two rational numbers.
In this case, we have the number 0.33... (periodic).
This is the decimal expression for one third:
[tex]0.33\ldots=\frac{0.99..}{3}=\frac{1}{3}[/tex]It is a rational number and it is equal to 1/3.
Observation: in the case we are talking about 0.3333333 (not periodic), it is a rational number also:
[tex]0.3333333=\frac{3,333,333}{10,000,000}[/tex]