5.46 to 3 sig figs means the range is {5.455,5.465} and 17.74 means the range {17.735,17.745}. p=q²/r has a maximum value when q=5.465 and r=17.735 and a minimum value when 5.455 and r=17.745. So the range of p is 1.6769 to 1.6840. When we have 2 decimal places we get p=1.68 which accommodates the maximum and minimum values of the range. So 2 decimal places is a suitable degree of accuracy, or we could say 3 significant figures.
