When representing decimal numbers that have infinite repetitions of its decimal digits we need to find the period, if the number has a period then it is a rational number, otherwise it isnt.
The period of a number is the part that always repeat, for instance in "2.666666..." the period is "6" and in "2.5050505050..." the period is "50". In the number given to us there is no period, because there is not a sign number that is always repeating, therefore it is not rational.