I have been thinking about a continuing decimal, i.e. 0.707007000700007...

obviously, the decimals composite parts are 0.7+0.007+0.000007+...

My question is this, is this decimal rational or irrational? And a reason why?

I first started thinking of geometrical progressions and summing to infinity, but I found that my common ratio, r, had to change to create the decimal, so I personally think it's irrational as the repeating block is changing? Does anyone have a neat proof of this or even better, think that I am wrong?

Kind regards, tom