Can pi be represented in a particular number base,so that it is no more an irrational number?
Pi representation in a different number base
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number-theory
elementary-number-theory
irrational-numbers
pi
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5No. Pi is an irrational number, it doesnt care how you represent it. – 2017-01-08
2 Answers
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No. The definition of rational number is independent of the base. The definition says that $x$ is irrational if and only if there doesn't exist a $p,q\in\mathbb{Z}$ such that $x=p/q$. No mention of bases.
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No.
In any base the "decimal" expansion of a number eventually repeats if and only if the number is rational: a quotient $a/b$ of integers. The only part of this that depends on the base is whether or not the decimal terminates (that is, is $0$ from some point on).
The irrationality of $\pi$ means it can't be expressed as a quotient $a/b$ of integers.