Using Conversion Factors
in Unit Analysis
(Dimensional Analysis)
Problem-solving method that uses the fact
that any number or expression can be
multiplied by one without changing its value
1 dozen eggs
12 eggs
or
12 eggs
1 dozen eggs
Doing Problems
1. Read problem completely
2. Determine the measured qty. in the
problem and the units
3. Determine units being requested
4. Determine conversion factor that will
allow you to change to the new unit
We will look at converting:
1. English units
2. English units to Metric Units
3. Metric units
Converting from English to English,
• 75 cookies is equivalent to how many
dozen cookies?
? dozen = 75 cookies 1 dozen
X
12 cookies
= 6.25 dozen
Series of unit factors – 2 possible
formats
Converting English Units
Converting English Units to
Metric Units
• How many centimeters are in 6.00 inches?
? cm = 6.00 inches X
2.54 cm
1 inch
= 15.24 cm
= 15.2 cm
Conversion of Metric Units
Remember the order of the units!
kilo
hecto
deca
Base
Unit
deci
centi
milli
micro
k
h
da
gram
(g)
d
c
m
μ
1000
100
10
liter (L)
0.1
0.01
0.001
0.000001
10-4
103
102
101
meter
(m)
10-1
10-2
10-3
10-5
10-6
Steps:
1.
2.
Given quantity w/its unit
Set up conversion factor
a.
b.
c.
d.
e.
3.
4.
Place given unit as the denominator of the conversion factor
Place desired unit as the numerator
Place a “1” in front of the large unit
Place a 10 in front of the smaller unit
Repeat b-d until reaching the final answer
Cancel Units – only the desired unit should be left
Solve the problem
An aspirin tablet contains 325 mg of active ingredient. How much
is this in cg?
325 mg
1
1 cg
10 mg
=
= 32.5cg of active ingredient
325 = 32.5 cg
10
• Convert 50.0 mL to liters?
50.0mL 1 cL
1
10 mL
1 dL
1 L = 50
10 cL 10 dL 1000
= 0.0500L