Question

Is 12.89 irrational

Answer 1

No.  It's the ratio of  1,289  to  100 .

Also, it can be written as a fraction with whole numbers
on top and bottom, like this:    1289 / 100 .

Also, it can be written down on paper completely, using
digits and a decimal point or fraction bar.  (You did that.)

Any one of these three facts makes it a rational number.