Dimensional Analysis

The correct scientific measurement for any physical quantity is represented by an accurate numerical value expressed with the desired SI unit.

Dimensional analysis, also known as the factor label method, is a mathematical approach that is based on the principle that the units of quantities must be subjected to the same mathematical operations as their associated numbers.

Often, a single physical quantity can be expressed in different, but equivalent, units. For instance, the length of an object can be expressed as meters or centimeters, where 1 meter represents the same amount of length as 100 centimeters.

Dimensional analysis facilitates the conversion between such equivalent units through the use of the unit conversion factor.

The unit conversion factor is a ratio between two different units that measure the same physical quantity.

For instance, length in meters or centimeters can be interconverted, using conversion factors: 1 meter per 100 centimeters, and 100 centimeters per 1 meter.

The ratio of choice depends on the desired unit in the result. Thus, to determine the length in meters, the correct unit conversion factor is the ratio that cancels the units of centimeters and lea