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