Question

How do you convert 0,5444444444 into a common fraction by first writing it as a geometric series...I tried it this way 0,5 (0,004+0,0004...)But it doesn't work out please help

Answer 1

Your decimals are not correct

0.5444444444
= .5 + .04 + .004 + .0004 + ...

let's leave the .5 sitting aside for the time being.

so we have
.04 + .004 + ...
a = .04, r = .1
sum of all = a/(1-r) = .04/(1-.1)
= .04/.9
= 4/90 = 2/45

now bring in the .5 or 1/2

so 0,5444444444
= 1/2 + 4/90
= 49/90

btw, that is not the easiest way to do this, but it was the method you needed.

Answer 2

Yes, I was confused, You put 0,5444444444. For future reference, use .'s