Question #42982

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Answer 1 · 2017-01-17T16:08:18

#0.090-9-0909...=1/11#
#0.88888...=8/9#
#0.06060606...=2/33#

(i) Let x =0.090909. Then,

100x=9.090909...=9+.090909...=9+x, So,.

99x=9, and so,# x =9/99=1/11#.

(ii) Let y = 0.8888..... Then,

10x=8.888...=8+x. So,

9x=8, and so, #x = 8/9#.

(iii) let z = 0.06060606... Then,

100x=6.060606...=6+x. So,

99x=6. And so, #x = 6/99=2/33#.