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Concept

Conversion Factor

A conversion factor is a fraction where the numerator and denominator represent the same quantity with different units. Example Conversion Factor [0.5em] 60 minutes/1 hour Recall that 1 hour and 60 minutes represent the same quantity. Multiplying a quantity by a conversion factor changes the quantity to an equivalent quantity in different units.

Given Quantity	Conversion	Result
2 hours	2 hours * 60 minutes/1 hour	120 minutes

The process of including units of measurement as factors is called dimensional analysis. Dimensional analysis can also be used when deciding which conversion factor will produce the target units.

Why

The Reason That the Quantities Are Equivalent

The numerator and denominator of the conversion factor represent the same quantity. This means that their quotient equals 1. Then, by the Identity Property of Multiplication, the amount of the given quantity does not change when multiplied by the conversion factor. Given Amount * 1 = Given Amount When converting from one unit to another, the target unit needs to be in the numerator of the conversion factor and the given unit needs to be in the denominator. Then when the quantity is multiplied by the conversion factor, the given unit will cancel out and the target unit will remain.

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