Attempt to view irrational number as a fractionI am wondering if an irrational number can be represented as a fraction in this way:For example (to represent π): π = 3.14159265359... = 314159265359... 100000000000... In the fraction 314159265359... 100000000000... , the numerator is an integer whose digits have the same order as digits of π, and the denominator is simply 10 ( # o f d i g i t s o f n u m e r a t o r − 1 ) . Isn't an irrational number represented as a fraction in this way? Probably I misunderstand the concept of the irrational number. Thanks in advance.

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Attempt to view irrational number as a fractionI am wondering if an irrational number can be represented as a fraction in this way:For example (to represent   π):  π  =  3.14159265359...  =      314159265359...    100000000000...  In the fraction       314159265359...    100000000000...  , the numerator is an integer whose digits have the same order as digits of   π, and the denominator is simply   10                (      #            o      f            d      i      g      i      t      s            o      f            n      u      m      e      r      a      t      o      r            −            1      )      . Isn&#039;t an irrational number represented as a fraction in this way? Probably I misunderstand the concept of the irrational number. Thanks in advance.

ebizsavvy1txn · Accepted Answer

If the numerator and denominator contains a finite number of digits each (and both are integers), then it&#039;s a rational number, but it won&#039;t equal   π. If they have infinitely many digits, then I don&#039;t know what the expression even means, but even if one could make sense of it, and the value would be   π, the numerator and denominator wouldn&#039;t be integers, and thus you wouldn&#039;t have a rational number, at least not a priori.

Uriah Molina · Accepted Answer

An irrational number is a number that can&#039;t be represented as a ratio (i.e., a fraction) of two integers.Since the digits of pi go on forever, your numerator is an infinite sequence of digits. That isn&#039;t an integer; only a finite sequence of digits defines an integer.Additionally, it&#039;s hard to know what your fraction means. You say the denominator is       10          # of digits of numerator      −      1      , but the number of digits in the numerator is infinite, so is your denominator       10          ∞      −      1      ? That isn&#039;t well-defined; it certainly isn&#039;t an integer.

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