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
Imperial – metric conversions
Conversion factors and unit
factors
Making conversions between different
units is very important
Always keep track of units in calculation
Conversion factor: 1000 mg = 1 g
Unit factors
1g
1
1000mg
1000mg
1
1g
There are two unit factors for any
conversion
Follow the units
Choose unit factor 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?
Conversion factor: 1 000 mg = 1 g
1g
Unit factor
1
1000mg
? g = amount in mg x unit factor
1g
? g  2680mg x
1000mg
Unit factor has value of 1 – no change in value
Unit factor causes old units to cancel
1g
? g  2680 x
 2.680 g
1000
Performing multiple
conversions
Apply each conversion factor sequentially,
constructing function with all units (and unit
factors) shown
Convert 515 m/s to mi/hr
Convert m → mi (m → km; km → mi)
Convert s → hr (s → min; min → hr)
 515 m  1 km  1 mi  60 s  60 min 
speed (mi/hr)= 
 3 



s
1.6093
km
1
min
1
hr

 10 m 



=1.15x103 mi/hr (3 S.F.)
Significant figures in conversions
S.F. must be limited by data not
conversion factors
Exact conversions have infinite S.F.
Inexact conversions use same or
more S.F.
 515 m  1 km  1 mi  60 s  60 min 
speed (mi/hr)= 
 3 



s
1.6093
km
1
min
1
hr
10
m






=1.15x103 mi/hr (3 S.F.)
Multiple dimensions
Each dimension in unit must be
converted
Volume provides example:
How many cm3 in 1 in3?
3
3
3
(2.54 cm) (2.54) cm 16.4 cm
=
=
3
3 3
3
(1 in)
1 in
1 in
1 cm = 10 mm
1 cm2 = 100 mm2
1 cm3 = 1,000 mm3
3
Let’s practice