Question

Why is pi an irrational number although it can be expressed in the form p\q i.e.22\7?

Answer 1

22/7 is an APPROXIMATION of the value of pi, not an exact representation. 22/7 is approximately 3.142857. A closer approximation of pi would be 3.14159265 which is correct out to 8 decimal places. You can see that this value differs from 22/7 starting in just the third decimal place. As such 22/7 is a fairly crude approximation of pi, but is probably good enough for many carpentry uses, but you should really use a little more precise value than 22/7 for anything that requires very high precision.

Pi is an irrational number, meaning that the decimal expansion of it never falls into a repeating pattern, though there are ways of calculating what any given digit of pi is and the digits of pi have been calculated out to millions upon millions of decimal places, far more than would be required to locate any single atomic particle in our known universe to ridiculous tolerances.

Unfortunately 22/7 is not quite up to this task (smile), nor is the second, slightly more accurate value I gave you. For any given calculation, you will need to use an approximation of pi that will give you a ‘good enough’ answer. One size does NOT fit all in this case.