Michelle, the way you asked the question suggests you don't maybe appreciate the difference among molecular, formula, and molar weights. They are not all "aka"! "Molecular" means "of one molecule"; "formula" means of one "formula unit", which is like a mole but is used for salts which don't have discrete molecules (i.e. each Na(1+) ion paired with a specific Cl(1-) ion) -- so, you take the written formula (e.g., NaCl) and treat it as if it were a molecule; and "molar" refers to having exactly one mole of your molecule (Avogadro's number of molecules).
And, relating to Susan's answer, it might be better to think of those MW values for the atoms as "elemental weights" since you're totalling them up as individual atoms. When you get the sum (191.317), that represents a mass, but at two different scales: the first, in units of Daltons (1 Dalton = 1/12 the mass of a 12C atom), is the mass of one assemblage (AgClO3) of atoms; the second, in units of grams (1 gram = 1/12 the mass of a mole of 12C atoms), is the mass of one Formula Unit of AgClO3 salt. These are two quite different scales: they differ by a factor of Avogadro's number (6.022 * 10^23), but you shouldn't let that stop you! Your body *mass* is the same, whether you *express* it in pounds (eew!) or in kilograms (yeah!) -- even though the particular numbers and units are different for these two ways. But when you use Daltons or grams, you just have to think for a minute, am I using Daltons and talking about one molecule, or am I using grams and talking about one mole of molecules? Once you're clear on that, then you can start thinking about expressing each type of quantity in the *"other"* type of unit; you'll need to divide or multiply by Avogadro's number to calculate that (as Susan did for you).
Hope this makes it clearer!