Converting Repeating Decimals to Fractions

[mahikakotecha]

Hi all,
I now that 0.66 repeating is 66/99
But how would you solve a repeating fraction, where the repetition is after a certain decimal; lets say 0.8666 which is actually 13/15
I tried solving it as 0.8 + 0.06 = 0.8 + 6/99
but that equals to 0.8606060 and not 0.866666

[Leaderboard]

@mahikakotecha

I now that 0.66 repeating is 66/99

0.66 = 66/100, not 66/99

(If you meant 0.\overline{6}, that’s not the same)

@mahikakotecha

But how would you solve a repeating fraction, where the repetition is after a certain decimal; lets say 0.8666 which is actually 13/15

Same process:

y = 0.8\overline{6}

10y = 8.\overline{6}

100y = 86.\overline{6}

Subtract the second from the third.

[mahikakotecha]

Thanks