Dimensional Analysis
Problem-solving method that uses the fact
that any number or expression can be
multiplied by one without changing its value
A BIT DIFFERENT THAN
USING PROPORTIONS!
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
Converting from English to Metric
Units and Vice versa
Use conversion factors that are exact by definition
1 inch = 2.54 cm
1 ounce = 28.35 g
1 quart = 0.946L or 946 mL
1 meter = 39.37 inches
1 kilogram = 2.2 pounds
Metric second = English second
1L = 1.0567 quarts
Conversion w/only 2 Units
Conversions with several units:
When it comes time to do the math, the first number
can be overlooked perhaps because it is visually
different and not in line with other values.
An error of omission is less likely using the following
non-fraction format:
Conversion of Metric Units Using
Dimensional Analysis
• Depends on how many units are between
the initial unit and the final unit
Conversion chart from larger to
smaller 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
Some Classroom Exercises
• A child weighs seven pounds at birth. How
many ounces is this?
• An aspirin tablet contains 325 mg of active
ingredient. How much is this in cg?
• One-fourth teaspoon has a mass of 0.21 g.
What is this mass in mg?
Some Classroom Exercises
• 32 grams is equal to ____________ kg
• 23 meters is equal to ____________ mm