How do you convert 0.6 (6 being repeated) to a fraction?

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Mar 4, 2016

Answer:

#0.bar(6) = 2/3#

Explanation:

Multiply by #10# to shift one place to the left and subtract the starting number to cancel out the repeating decimal.

To do this multiply by #(10-1)#:

#(10-1) * 0.bar(6) = 6.bar(6) - 0.bar(6) = 6#

Then divide both sides by #(10-1)# to find:

#0.bar(6) = 6/(10-1) = 6/9 = (color(red)(cancel(color(black)(3)))*2)/(color(red)(cancel(color(black)(3)))*3) = 2/3#

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