Another Phys with Calc problem

Hey again all, this time my problem is how to start this problem:

One molecule of water (H2O) contains two atoms of hydrogen and one atom of oxygen. A hydrogen atom has a mass of 1.0 u and an atom of oxygen has a mass of 16 u, approximately. (a) What is the mass in kilograms of one molecule of water? (b) How many molecules of water are in the world's oceans, which have an estimated total mass of 1.4 × 1021 kg?

It's obvious that once I've got the answer to part a, part b is easy. However, my theory as to how to solve part a seems too simple to work. If I'm told that a molecule of water contains two hydrogen atoms and one oxygen atom, and that 1 hydrogem atom = 1 u whereas 1 oxygen atom = 16 u... is the answer to part a as simple as converting 18u to kilograms? Trying it that way seems to come up with an incredibly large decimal so I'm skeptical as to whether or not my theory is correct. Please help.
 
I will give you an answer to first question. You have certainly seen the number 6.022*10^23. We get this number when we just divide 1g by u (in grams).
1/u=6.022*10^23
So if something weighs 18u it means that it weighs 18/6.022*10^23 grams. And that is 18/6.022*10^26 kilograms.
 
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