Question 961651
Fit this to geometric series.

{{{0.5555repeating=5(1/10+1/100+1/1000+1/10000+continued)}}}

{{{5(1/10^1+1/10^2+1/10^3+1/10^4+continued)}}}

{{{5((1/10)/(1-1/10))}}}

{{{5((1/10)/(9/10))}}}

{{{5(1/9)}}}

Perform the long division and you will find {{{1/9=0.11111repeating}}}.
You could then see that {{{5(0.11111repeating)=0.5555repeating}}}.


{{{highlight(5(1/9)=highlight(5/9))}}};
You can check this through long multiplication again if you want to be sure.
5 divided by 9 will give 0.555555.....