Conversion arithmetic is easy. Multiply by a factor, and the factor never changes. The errors that actually cost money almost never come from the multiplication: they come from picking the wrong factor, usually because two different units share a name.
Ounces that are not the same ounce
There are three units in common use called an ounce. The avoirdupois ounce is the everyday one for food and post, at 28.35 grams. The troy ounce, used for gold and silver, is about 31.1 grams, roughly ten per cent heavier. The fluid ounce is not a weight at all: it measures volume.
The precious metals case is the expensive one. Pricing gold with the everyday ounce understates the weight by around ten per cent, which on a metal priced per ounce is not a rounding difference. The ounce to gram calculator uses the avoirdupois ounce, and says so on the page for exactly this reason.
Cups, which depend on the country
A US cup is 8 US fluid ounces, about 236.6 mL. A metric or Australian cup is 250 mL. A UK Imperial cup is different again. For most cooking the difference is absorbable, but in baking, where ratios do the work, a six per cent error compounds across every ingredient in the recipe.
The safest habit is to convert to grams or millilitres once, at the start, and work from there. The cup to mL converter asks which cup standard you mean rather than assuming one.
Tons that are three different weights
A metric tonne is 1,000 kg. A US short ton is about 907 kg. A UK long ton is about 1,016 kg. Anywhere materials are bought by the ton, soil, gravel, steel, freight, the gap between the largest and smallest is over ten per cent of the delivery.
Gallons, which differ by about 20 per cent
A US gallon is 3.785 litres; an Imperial gallon is 4.546 litres. Fuel economy figures quoted in miles per gallon are not comparable between the two without saying which gallon is meant, and the difference is large enough to change which car looks more efficient.
The habit that prevents all of them
Write the unit next to every number, including the intermediate ones. Most conversion errors survive because the units get dropped somewhere in the middle of the working, and a bare number carries no evidence of what it measures. If the units are still attached at the end, they either cancel correctly or they visibly do not.
The second habit is to sanity-check the direction of the answer. Converting to a smaller unit should give a bigger number. Getting that backwards is the single most common conversion slip, and it takes a second to catch.