Between a rational and a irrational

[nerdy_time]

Hello.
Between a rational and a irrational is there a rational? and a irrational? and vice-versa?
I know that between 2 rationals there is a rational and a irrational and that between 2 irrationals there is a rational and a irrational, but i cannot figure this out... please help.
Thanks.

 

[slider142]

Let I be the irrational number and r be the rational number. If I > r, consider the number d = I - r.

 

[tim_lou]

between any two unequal number there is a rational and irrational number. It's easiest to see this in decimal representation.