Notice that [tex]0.272727\ldots=\dfrac{27}{99}=\dfrac{3}{11}[/tex] is rational
and [tex]0.1010010001\ldots[/tex] is irrational as this is non-terminating and non-repeating.
Since sum of rational and irrational is always irrational, [tex]x[/tex] is irrational.
