How do I express 0.999(9) as a fraction?I'm noob in math. If 0.333(3) is 1/3, 0.666(6) is 2/3, then 0.999(9) is what?If 3/3 and 0.999(9) is the same, then how can I express one of them without expressing the other?

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How do I express 0.999(9) as a fraction?I&#039;m noob in math. If 0.333(3) is 1/3, 0.666(6) is 2/3, then 0.999(9) is what?If 3/3 and 0.999(9) is the same, then how can I express one of them without expressing the other?

Gemma Conley · Accepted Answer

Well, notice that:                    (1)                              n          1                :=        0.333        ⋯        =        0.                  3          ¯                =                  1          3                    So, when we muliply       n    1   by two, we get:                    (2)                              n          2                :=        2        ⋅        0.333        ⋯        =        0.666        ⋯        =        0.                  6          ¯                =                  2          3                    So, when we muliply       n    1   by three, we get:                    (3)                              n          3                :=        3        ⋅        0.333        ⋯        =        0.999        ⋯        =        0.                  9          ¯                =                  3          3                =        1            Where       x    ¯   means a repeating decimal.

kaeisky9u · Accepted Answer

0.999  …  =  1Proof: Let   x  =  0.999  … . Now consider that   10  x  =  9.999  … . So then we have that   9  x  =  10  x  −  x  =  9.99  …  −  0.999  …  =  9.0Thus   9  x      /    9  =  9      /    9  =  1

How do I express 0.999(9) as a fraction? I'm noob in math. If 0.333(3) is 1/3, 0.666(6) is 2/3, then 0.999(9) is what? If 3/3 and 0.999(9) is the same, then how can I express one of them without expressing the other?

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