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Answer 1 · 2017-08-22T04:36:22

#31/15#

So you want #6# to be recurring. This is shown as #2.0dot6dot6#.

We set this equal to #x#.

#x=2.0dot6dot6#

Multiply by #10#

#10x=20.dot6dot6#

Multiply by #10# again

#100x=206.dot6dot6#

Now we know what #10x# and #100x# is equal to. Then, subtracting #10x# from #100x# will get rid of the #.dot6dot6# (Annoying part)

#90x=186#

Divide by #90#

#x=31/15#

Now since we set #x=2.0dot6dot6#,

#2.0dot6dot6=31/15#

And bob's your uncle.
Hope this helped! ;)