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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?

Zara_me
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    https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational – Angina Seng May 27 '19 at 17:02
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    $\pi$ isn't really $\frac {22}7$, that's just an approximation. $\pi= 3.14159265358979\cdots$ while $\frac {22}7=3.\overline {142857}$ – lulu May 27 '19 at 17:02
  • I have not calculated 22/7 but it it non terminating recurring? – Zara_me May 27 '19 at 17:09
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    If you believe that $\pi$ is $\frac{22}{7}$ then why not take $p=22$ and $q=7$? – John Douma May 27 '19 at 17:35
  • 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 https://www.mathsisfun.com/irrational-numbers.html – NoChance May 27 '19 at 19:54
  • Ok so it is non terminating and non recurring digits after decimal point which makes it irrational. – Zara_me May 29 '19 at 05:06

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“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

user328442
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