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 $S_oo = a/(1-r)$

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

$= (4/10)/(9/10)$

$= 4/9$

How to find the fractional notation for the given infinite sum below? 0.bar40.bar4 = 4/104/10 + 4/1004/100 + 4/10004/1000 + 4/100004/10000 +.....