How to find the fractional notation for the given infinite sum below? #0.bar4# = #4/10# + #4/100# + #4/1000# + #4/10000# +.....

2 Answers
Jul 5, 2018

The answer is #=4/9#

Explanation:

Let

#X=0.4444444444....#

Then,

#10X=4.4444444....#

Therefore,

#10X-X=4.4444444..-0.4444444....=4.00000#

#9X=4#

#X=4/9#

Jul 5, 2018

# = 4/9 #

Explanation:

Notice how this is a geometric series with first term, #a = 4/10#
and a common ratio of #1/10 #

We know #S_oo = a/(1-r) #

#= (4/10 )/ (1-1/10) #

# = (4/10)/(9/10) #

# = 4/9 #