Question

Is 3.80012569923.... a irrational or rational ?

Answer 1

We can't tell from the information you've given.

With the dots at the end, you showed that there's more
to the decimal.  But you didn't say how much more.

-- If the decimal EVER ends, even after a billion places,
then it's rational.

-- If it repeats, then it's rational.  That .80012569923 may repeat,
or part of it, like the 9923, may repeat, or the whole thing may be
part of some larger bunch that repeats.  We don't know.