I've seen websites that show the ratios of the 10 most common elements but they compare them by relative mass. I think it's more interesting to know the relative abundances of atomic nuclei because that is what you need to know to understand why the universe has the chemical makeup that it does. What are the 10 most abundant elements in the universe by number of atomic nuclei?
All right, so I took the first list on wikipedia listing the 10 most common elements by mass in parts per million, and did what Rob recommended and here's what I got.
Hydrogen - 739000amu(H)/1amu(H)=739000 H atoms
Helium - 240000amu(He)/4amu(He)=60000 He atoms
Oxygen - 10400amu(O)/16amu(O)=650 O atoms
Carbon - 4600amu(C)/12amu(C)=383 C atoms
Neon - 1340amu(Ne)/20.1amu(Ne)=66 Ne atoms
Iron - 1090amu(Fe)/55.845amu(Fe)=19.5 Fe atoms
Nitrogen - 960amu(N)/14amu(N)=68.5 N atoms
Silicon - 650amu(Si)/28.1amu(Si)=23 Si atoms
Magnesium, - 580amu(Mg)/24.3amu(Mg)=24 Mg atoms
Sulfur - 440amu(S)/32.1amu(S)=13.7 S atoms
So therefore, the 10 most common elements in the universe by atom, with the relative ratios between them, is;
1.Hydrogen (739000) 2.Helium (60000) 3.Oxygen (650) 4.Carbon (383) 5.Nitrogen (68.5) 6.Neon (66) 7.Magnesium (24) 8.Silicon (23) 9.Iron (19.5) 10.Sulfur (13.7)
If anyone sees a mistake that I made with my reasoning or calculations then please point it out.