First convert milligrams to grams by dividing it by 1000. This gets us 0.0564 grams of iridium. Since we know the ratio between one iridium atom and grams is 1 atom/3.19*10^22 grams, use that ratio as the conversion factor in dimensional analysis. 0.0564 grams * (1 atom/3.19*10^22 grams). Grams cancel out and we are left with 1.77*10^20 atoms.