Unit Analysis
(or 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 quantities 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
Rules
1. You must use Dimensional Analysis to
solve conversion problems
2. Always show all your work
3. Include units
4. Make sure your units cancel out
5. Everything on the top is multiplied
Everything on bottom is divided from the top
Conversion Factors
• A ratio (or fraction) derived from the
equality between two different units that
can be used to convert from one unit to
the other.
• Conversion factors always equal one
because the two values are equal to each
other.
Conversion Factors
4 quarters
1 dollar
=1
=1
1 dollar
4 quarters
60 minutes
1 hour
=1
=1
1 hour
60 minutes
1m
100 cm
=1
100 cm
=1
1m
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
Convert 62.0 inches to centimeters
• First we need to map out what we are
doing.
62.0 in  ___ cm
Convert 62.0 inches to centimeters
• Second we need to determine our
conversion factor
How many centimeters are in one inch?
2.54 cm = 1 in
1 in
2.54 cm
=1
2.54 cm
1 in
=1
Note: We could have also
used that 1cm = .394 inch
but as a general rule, the
larger unit gets the 1!
Convert 62.0 inches to centimeters
• Third, we multiply our given by the
conversion factor…making sure to arrange
the conversion factor so that the units
CANCEL!
62.0 in X 2.54 cm
= 157.48 cm
1 in
Note: Units that are both on the top and the
bottom cancel
Convert 62.0 inches to centimeters
• Lastly, we make sure that we reached our
“destination” and that we have the correct
number of significant figures.
157.48 cm  157 cm
Note: Conversions factors do not follow
significant figure rules, they are not
measured and do not show accuracy.
Multiple Conversions
• When conversions require several steps,
Dimensional Analysis is extremely useful.
It helps organize information so we can
think through problems step-by-step.
How many feet are in 965 cm?
• 1. Map it out: 965 cm  ___ ft
• 2. Find conversion factors:
How many feet are in 965 cm?
965 cm
X
1 in
2.54 cm
X
1 ft
12 in
= 31.66  31.7 ft
Conversion w/only 2 Units
Conversions with several units:
You are cooking for a large group of
people. You must change the recipe to
accommodate all the guests. How many
gallons will 384 teaspoons of vanilla
extract occupy?
– 1 Tablespoon (T) = 3 teaspoons (t)
– 1 cup (c) = 16 Tablespoons
– 1 pint (pt) = 2 cups
– 1 quart (qt) = 2 pints
– 1 gallon (gal) = 4 quarts