Question

If irrational number cannot be expressed in the form p/q where p and q are integers, and q is not = 0, then why pi is irrational though it is represented in the form p/q

Answer 1

No. The definition of irrational number itself tells that it cannot be expressed in the form of p/q (q not equal to 0), where p and q are integers.

Examples:

The value of pi = 3.1415926535897932384626433…
The value of square root of 2 = 1.4142135
Log value of 3 = 0.47712125472…
Many trigonometric values of angles such as sine 85 degree, tan 37 degree etc.., are irrational numbers.
All the values in the above examples have non-recurring non-terminating decimal which cannot be expressed as a fraction.

Note: pi is not equal to 22/7(but 22/7 is an approximate value).
MORE SUITABLE DEFINATION OF irrational number is that it has non terminating non recurring decimal expansion.


Any irrational number cannot be expressed as p/q , q not equal to 0. According to the defination of rational numbers, any number which can be expressed in form of p/q where q is not equal to 0 is a rational number. Even π= (22/7) is the estimated value of 3.14..{which is not repeating and non recurring..}