Dimensional Analysis The importance of units in calculations

Conversion factors Making conversions between different units is very important Always keep track of the units Conversion factor equates two different units

Unit factors Make use of unit factors There are 1000 mg in 1 g (conversion factor) 1000 mg/1 g = 1 1 g/1000 mg = 1 There are two unit factors for any conversion factors

Follow the units Arrange conversion to eliminate the given unit

Unit factors at work How many grams are there in 2680 mg of sucrose? We know there are mg in 1 g 1 g/1000 mg = 1 (unit factor) ? g = amount in mg x unit factor Unit factor has value of 1 – no change in value Application of unit factor causes old units to cancel Never forget to show units of any measurement – unless it is a unit-less quantity

Performing multiple conversions Apply each conversion factor sequentially, constructing a function with all units (and unit factors)

Multiple dimensions Each dimension in a unit must be converted Volume provides an example 1 cm = 10 mm 1 cm 2 = 100 mm 2 1 cm 3 = 1,000 mm 3