is -.06006000600006 a rational or irrational number

Answer 1

I do not know of any trick to prove it rational, so suspect it is irrational.

Answer 2

If the number is

-.06006000600006....

I.e. the decimal expansion does not terminate and the number of zeroes increases by one between the sixes, then the number is irrational because the decimal expansion of a rational number must either terminate or be periodic.