I believe conversion factors have an infinite number of significant figures. They should be exact values; but not all of them are, are they?
I looked at a pdf document (via the Internet Archive) and it agreed with the fact that all conversion factors have an infinite number of significant figures.
I know this is true with a conversion factor such as $\frac{\pu{1 cal}}{\pu{g ^\circ C}}$, because this is how a calorie is defined. Similarly, it's the same for $\frac{\pu{1 kg}}{\pu{1000 g}}$, $\frac{\pu{4 quarts}}{\pu{gal}}$, etc.. We know these are exact, and in dimensional analysis, if you multiplied by the first conversion factor, you wouldn't end up with one significant figure because of the single significant figure in $\pu{1 cal}$.
However, what is the case with measured conversions, such as $\frac{\pu{4.184 J}}{\pu{cal}}$ or $\frac{\pu{1.60934 km}}{\pu{mi}}$? These were measured using significant figures, so it would make sense to round with significant figures when multiplying (dimensional analysis), but the above link says otherwise.
What should I do, especially with the below type of conversions?