How do you change 0.244444444 into a fraction?

2 Answers
Nov 6, 2015

This is the technique also for dealing more difficult ones. You have to decide what to multiply by guided by the repeat cycle.

Explanation:

Let #x = 0.244444....#..............(1)

so #10x = 2.44444#.....(2)

(2) - (1)

#10x -x=2.2#
#9x =2 2/10#

#x= 2/9 + 2/90#

#x = (20+2)/90#

#x=22/90#

#x=11/45#

Nov 6, 2015

Convert into a terminating continued fraction, then simplify to find

#0.2dot(4) = 11/45#

Explanation:

#0.2dot(4)# is less than #1# so the continued fraction starts #0 + 1/...#

Calculate #1/(0.2dot(4)) = 4.dot(0)dot(9)#

So our continued fraction looks like #0+1/(4+1/...)#

Subtract #4# then calculate #1/(0.dot(0)dot(9)) = 11#

So our fraction terminates here in the form: #0+1/(4+1/11)#

#0+1/(4+1/11) = 1/(44/11+1/11) = 1/(45/11) = 11/45#