Question

Calculate the concentration of the initial nitrate stock solution (in ppm) if exactly 0.361 g of
KNO3 is dissolved in a 1 L volumetric flask with distilled water.

Answer 1

I assume you mean ppmw (ppm by mass and not by volume)

So mass H2O in that 1 L is 1000 g and that added to the 0.361 gives you a mass of solution of 1000.361g.
0.361g x (1E6/1000.361) = ? ppmw and you round that off to three significant figures and you get the same answer as if were calculated as ppmv.
1 ppm = 1 mg/L
0.361 g = 361 mg, so 361 ppmv