Question

A classmate says that 0.285714 repeating  is not a rational number because it does not terminate. Explain her error.   

I need help answering this

Answer 1

A number that is repeated periodically is an irrational number! Error lies in the fact that if we have a decimal value and a string repeat it (at some time) it is an irrational number, that is, it can not be represented as a fraction. It is scientifically proven.

Answer 2

It is a rational number because it can be put into a fraction using ordinary whole numbers.

On the other hand a fraction containing ordinary whole numbers isn't available for pi. Therefore, pi is irrational.