Unit conversion is multiplication by a carefully chosen form of the number one. A conversion factor such as 1 inch = 2.54 cm can be written as a fraction equal to 1, and multiplying by it changes the units without changing the quantity.
Track the units, not just the numbers
Write the units into the working and cancel them like algebraic symbols. If the answer comes out in the units you wanted, the arrangement was right; if it comes out in metres per second when you wanted seconds, you have divided where you should have multiplied. This is called dimensional analysis and it catches most conversion errors before they matter.
Exact versus approximate factors
Some conversions are exact by definition: an inch is exactly 2.54 cm, a pound is exactly 0.45359237 kg, and a nautical mile is exactly 1852 m. Others are measured constants and carry uncertainty. Where a factor is exact, the only error in your answer is the one you introduced by rounding.
Temperature is different
Every other conversion here is a pure scaling, so zero maps to zero. Temperature scales have offset zero points, which is why Fahrenheit needs both a multiplication and a subtraction. It also means temperature differences convert differently from temperature values: a rise of 10 °C is a rise of 18 °F, not 50 °F.
The decimal versus binary trap in data sizes
A kilobyte is 1000 bytes; a kibibyte is 1024. Drive manufacturers use the decimal prefixes and most operating systems report the binary ones, which is why a “1 TB” drive shows as about 931 GB. Both figures are correct — they are measuring in different units with confusingly similar names.
Why unit errors are expensive
The Mars Climate Orbiter was lost in 1999 because one team supplied thrust data in pound-force seconds while the receiving software expected newton-seconds. The arithmetic was fine; the units were not.