Help with numbers

[JDO]

I have recently seen some stats that describe pot odds using "underdog" drawing odds and that doesn't seem like an accurate way to describe pot odds.

My problem is best explained with an example. Limit poker. I'm, 4 to a flush, and I want to decide if it is in my interest to call. For simplicity, if I don't hit my card on the turn, I'l fold.

So my probability of making my flush is 9:47. Or I am a 38:9 underdog to catch my hand. Do I need 47:9 (or 5.2:1) odds to call or 38:9 (or 4.2:1)?
My mind is stuck thinking that I need 47:9 and here's why: If you have X good cards of all possible cards Y. Then your chances of making your hand are X/Y. So your chances of not making your hands are Y/X. In this case, I'll make my hand 1:5.2 times and won't make it 5.2:1 times, so I need at least 5.2:1 (including my bet) from the pot to make it a good call. Not 4.2:1.
Am I right?