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

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Answer 1 · 2018-07-05T07:40:07

The answer is #=4/9#

Let

#X=0.4444444444....#

Then,

#10X=4.4444444....#

Therefore,

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

#9X=4#

#X=4/9#

Answer 2 · 2018-07-05T09:00:47

# = 4/9 #

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 #