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How can you tell if a number is rational or irrational?

a) 3.215 (there is a line drawn over the 15)
b.) square root 10
c) 0.143639854024

can you please explain what i need to look at to tell which is which?

  • math - ,

    any number whose decimal expression terminates or ends in a repeating group of digits is rational. Otherwise, probably not.

    (a) 3.21515151515...
    3 + 2/10 + 15/990 is rational

    To find out what .0151515... is, let it be x

    x = .015151515...
    10x = .151515
    1000x = 15.15151515...
    subtract 10x from 1000x:
    990x = 15
    x = 15/990

    (b)the square root of any number which is not a perfect square is irrational

    (c) If that's exact, it terminates and is rational
    (d) same

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