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?

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    $\begingroup$ en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational $\endgroup$ – Lord Shark the Unknown May 27 at 17:02
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    $\begingroup$ $\pi$ isn't really $\frac {22}7$, that's just an approximation. $\pi= 3.14159265358979\cdots$ while $\frac {22}7=3.\overline {142857}$ $\endgroup$ – lulu May 27 at 17:02
  • $\begingroup$ I have not calculated 22/7 but it it non terminating recurring? $\endgroup$ – Zara_me May 27 at 17:09
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    $\begingroup$ If you believe that $\pi$ is $\frac{22}{7}$ then why not take $p=22$ and $q=7$? $\endgroup$ – John Douma May 27 at 17:35
  • $\begingroup$ The reason is that pi is classified as an irrational number. Simply put, it has non ending sequence of dissimilar digits after the decimal point and does not even get closer to a specific rational value. Only Rational numbers can be written as a/b. See mathsisfun.com/irrational-numbers.html $\endgroup$ – NoChance May 27 at 19:54

“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


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