unit conversion

Unit conversion is rewriting the same physical quantity in a different unit, like 2 kilometres as 2000 metres, or 60 miles per hour as about 27 metres per second. The thing measured does not change; only the number and the unit-name do, because you are counting in bigger or smaller steps.

The reliable method is to multiply by a conversion factor equal to 1. Because 1000 m = 1 km, the fraction (1000 m)/(1 km) equals 1, and multiplying by 1 never changes a quantity's value. So 2 km times (1000 m / 1 km) = 2000 m; the 'km' cancels top and bottom, leaving metres. Chain several such factors to go from, say, km/h to m/s: 90 km/h times (1000 m / 1 km) times (1 h / 3600 s) = 25 m/s.

Treating units as algebraic symbols that cancel is the safest way to avoid multiplying when you should divide. It also connects to dimensional analysis: if the units do not cancel down to what you expect, you have set the conversion up upside-down.