How do you convert #0.916# repeating to a fraction?

1 Answer
Aug 13, 2016

#0.91bar(6) = 11/12#

Explanation:

If you meant #0.91bar(6) = 0.916666...# then first multiply by #100(10-1) = 1000-100#. The factor #100# is to shift the number #2# places to the left to leave the repeating portion just after the decimal point. The factor #(10-1)# is to shift it one further place to the left (the length of the repeating pattern), then subtract the original to cancel out the repeating tail...

#(1000-100)0.91bar(6) = 916.bar(6) - 91.bar(6) = 825#

Then dividing both ends by #(1000-100)# we find:

#0.91bar(6) = 825/(1000-100) = 825/900 = (color(red)(cancel(color(black)(75)))xx11)/(color(red)(cancel(color(black)(75)))xx12) = 11/12#