Recall, is defined as the ratio of the circumference (say c) of a circle to its diameter (say d).
That is, . This seems to contradict the fact that is irrational. How will you resolve this contradiction?
There is no contradiction. When we measure any length with ruler or any other device, we only get an approximate rational value. We never get an exact value. So, c or d is irrational when we are actually writing approximate rational values of c and d. So, the fraction is irrational.