Let us remind the concept of Rational Numbers. Rational numbers are the Ratio of two different unified integers. Or in other words, we can say that rational numbers are simply the ratio of two numbers with no common factor in them. Now, any fractional number may be a rational number or may not be, it depends on the nature of the fractional number that is whether the number has finite number after decimal or not. If any fractional number is re-written as the simplified ratio then it is a rational number.
Let us discuss about the number pi. Now, if we see the value of it is approx 3.14159265.... That is it has an infinite decimal places as the value of pi is no finite. Since the pi is an infinite number (after decimal) or the value after the decimal is non – terminating (that means the value has no end), therefore the number 3.14159265 cannot be displayed as a ratio of two integers. Since the value of pi that is also written as ( 22 / 7 ) but this value is not perfect that is it is an approximate value, the actual value of pi is 3.14159265 and it is an non – terminating number, there fore pi is not an rational number. Irrespective of the value of pi that is 22/7 it is not considered as a rational number as the actual value of pi is 3.14159265 which is not a rational number. Therefore the number pi is not a rational number.