MathematicsExpress 0.99999…. in the form p/q . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

Express 0.99999…. in the form p/q . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

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    Solution:

    Assume that x = 0.9999…..Eq (1)

    Multiplying both sides by 10,

    10x = 9.9999…. Eq. (2)

    Eq.(2) – Eq.(1), we get

    10x-x = 9.9999…- 0.9999…

    9x = 9

    x = 1

    The difference between 1 and 0.999999 is 0.000001 which is negligible.

    Hence, we can conclude that, 0.999 is too much near 1, therefore, 1 as the answer can be justified.

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