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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 desired _ unit Given _ unit _ x desired _ unit given _ unit Unit factors at work How many grams are there in 2680 mg of sucrose? We know there are 1 000 mg in 1 g 1 g/1000 mg = 1 (unit factor) ? g = amount in mg x unit factor 2680mgx1g ?g 2.680 g 1000mg 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) 515m 1km 1mi 60 s 60 min speed (mi / hr ) 3 s 10 m 1.6093 km 1min 1 hr 1.15 x103 mi / hr Multiple dimensions Each dimension in a unit must be converted Volume provides an example (2.54cm)3 (2.54)3 cm3 16.39cm3 3 3 3 (1in) 1 in 1in3 1 cm = 10 mm 1 cm2 = 100 mm2 1 cm3 = 1,000 mm3