Is 12.52 (rounded to 2 d. p.) is rational or irrational

Yes. Rational numbers are those numbers that can be still expressed in standard form or in fraction form and vice-versa. Unlike irrational numbers that are opposed to the definition of rational numbers. These values include pi, square root of two and etc. These values are impossible to fractionize. To better illustrate this circumstance. 

We can have calculate a number that will have a quotient of 0.634 or a fraction that is equal to the given value. 
1.  634/1000 = 0.634 
2.  317/500 = 0.634
3. 313/25 = 12.52