A physical unit serves to numerically express a physical quantity in terms of how it compares to some standard quantity. Physical units have precise definitions that are periodically updated as instrumentation and theory improves.
Some properties of units include:
- Quantites that are expressed in different units cannot be added unless they are measuring the same type of physical quantity (i.e. length). They can not, however, be added until the units are converted so that they are the same.
- When a unit is divided by itself, the division yields a unitless 1.
- When two different units are multiplied by each other, the result is a new unit. For instance, in SI the unit of momentum is one kilogram multiplied by one meter divided by one second. See also dimensional analysis.
- Conversion from a given unit in to a different unit can be accomplished in the following fashion:
- Take a known fact relating the given unit to the desired unit (for instance, 1 mile = 5280 feet and 1 hour = 3600 seconds).
- Next use the above equations to construct a fraction that has a numerical value of one and that has units that, when multiplied with the original quantity, will cancel the original units (for instance: given a quantity in feet per second that I want to convert in to miles per hour, I would change the above two equations to 1 = (1 mile) / (5280 feet) and 1 = (3600 seconds) / (1 hour))
- Last, multiply the original quatity by the fractions, called conversion factors, to obtain the same quantity expressed in different units.
Note: since the conversion factors have a numerical value of one, multiplying any quantity by them will not change that quantity's value.
The SI system of units is the one which is most widely used by scientists.