how do I convert 508 seconds into minutes?

I know I divide 508 by 60 and I get 8.466666667, so that is 8 minutes and then everything behind the decimal point. But how do I get all of that behind the decimal point into seconds?

.4666666... = 4/10 + 2/30 = 14/30

14/30 min = 28 seconds

where did the 4/10 and 2/30 come from, and then how did you get 14/30 min = 28 seconds, because minutes and seconds are not the same thing. This doesn't make any sense to me, I'm sorry.