Why cannot pi value 22/7(3.14..) be written in $p/q$ form?

Question

Since a rational number e.g 1/4 or -1/4 can be written in form of $p/q$, why cannot we write irrational $pi$ value which is also $22/7$ ,in form of p/q?

Answer 1

“why cannot we write irrational pi value which is also 22/7...”

It is true that $\pi$ is irrational but then this implies that $\pi$ cannot be rational and hence cannot be written as a fraction of two integers such as $\frac{22}{7}.$

For a wonderful proof (techniques of elementary calculus used here), see https://projecteuclid.org/download/pdf_1/euclid.bams/1183510788