How do you convert 3.2 (2 being repeated) to a fraction?

1 Answer
Mar 7, 2016

#3.bar(2) = 29/9#

Explanation:

Using the notation of a bar over a set of digits to denote their infinite repetition,

let #x = 3.bar(2)#

#=> 10x = 32.bar(2)#

#=> 10x - x = 32.bar(2)-3.bar(2) = 29#

#=> 9x = 29#

#:. x = 29/9#

This technique works in general. Set #x# as your desired value, multiply by #10^n# where #n# is the number of digits repeating, and then subtract #x# to eliminate the infinitely repeating portion. It then is just a matter of dividing by #10^n-1# and reducing the resulting fraction.