How do you change 0.244444444 into a fraction?
This is the technique also for dealing more difficult ones. You have to decide what to multiply by guided by the repeat cycle.
(2) - (1)
Convert into a terminating continued fraction, then simplify to find
#0.2dot(4) = 11/45#
So our continued fraction looks like
So our fraction terminates here in the form:
#0+1/(4+1/11) = 1/(44/11+1/11) = 1/(45/11) = 11/45#