Most of these factors are exact
It surprises people that conversion between metric and imperial units involves no uncertainty at all. Since the 1959 International Yard and Pound Agreement, an inch is 2.54 centimetres and a pound is 0.45359237 kilograms — not approximately, but by definition. The standards bodies of six countries agreed the numbers, and every other imperial length and weight follows from them.
So any imprecision in a converted figure comes from rounding the answer, never from the factor. Each page states its factor in full and says whether it is exact, which is why several of them carry more decimal places than you will ever need.
The mistakes worth knowing about
Four traps account for most conversion errors, and each has a page here devoted to it. Two units sharing a name: US and Imperial gallons differ by 20%, and confusingly the fluid ounces differ by 4% in the opposite direction. Squared factors: area does not convert with the length factor — using 0.3048 instead of 0.0929 for square feet gives an answer three times too large. Inverse relationships: mpg and L/100km measure opposite things, so doubling one halves the other. Mixed notation: 5 feet 10 inches is not 5.10 feet, and 11 stone 4 is not 11.4 stone, because the smaller unit is out of twelve or fourteen rather than ten.
A fifth is not really a conversion at all: cups to grams has no single answer, because cups measure volume and grams measure mass. A cup of flour and a cup of honey differ by a factor of nearly three, so that page asks which ingredient you mean.
Frequently asked questions
Are these conversion factors exact?
Most are. Since 1959, factors such as 1 inch = 2.54 cm and 1 pound = 0.45359237 kg are definitions rather than measurements, so they carry no uncertainty. Each page states whether its factor is exact.
Why do US and Imperial units differ?
Britain redefined several units in 1824, after America had already adopted the older English definitions at independence. So the split came from Britain changing, not America deviating.