Introduction to
Chemistry
for Allied Health Sciences
Dimensional Analysis
Kirk Hunter
Chemical Technology Department
Texas State Technical College Waco
Dimensional
Analysis
Dimensional Analysis
(Factor-Unit Method)
• A simple, powerful tool.
• Converts among measurements
expressed in different units.
• Develops relationships between units
and expresses this relationship as a
factor of both units.
Dimensional Analysis
(Factor-Unit Method)
• Example:
– 500 grams is equivalent to how many
pounds?
Dimensional Analysis
(Factor-Unit Method)
• Example:
– 500 grams is equivalent to how many
pounds?
Step 1: Write the statement as a mathematical formula.
500 gram s CF  ______ pounds
Dimensional Analysis
(Factor-Unit Method)
• Example:
– 500 grams is equivalent to how many
pounds?
Step 2: Write the relationship between the known and
unknown units.
1 pound = 454 grams
Dimensional Analysis
(Factor-Unit Method)
• Example:
– 500 grams is equivalent to how many
pounds?
Step 3: Write the relationship as two ratios.
454 gram s
1 pound
1 pound
454 gram s
Dimensional Analysis
(Factor-Unit Method)
• Example:
– 500 grams is equivalent to how many
pounds?
Step 4: Select the relationship that has the unit sought on
top.
454 gram s
1 pound
1 pound
454 gram s
500 gram s CF  ______ pounds
Dimensional Analysis
(Factor-Unit Method)
• Example:
– 500 grams is equivalent to how many
pounds?
Step 4: Select the relationship that has the unit sought on
top.
1 pound
500 gram s
 ______ pounds
454 gram s
Dimensional Analysis
(Factor-Unit Method)
• Example:
– 500 grams is equivalent to how many
pounds?
Step 5: Perform the calculation.
1 pound
500 gram s
 1.10 pounds
454 gram s
Dimensional Analysis
(Factor-Unit Method)
• Example:
– 500 grams is equivalent to how many
pounds?
Step 6: Check the answer. Is it reasonable?
1 pound
500 gram s
 1.10 pounds
454 gram s
Dimensional Analysis
(Factor-Unit Method)
• Example:
– A can of Coca-Cola contains 12 fluid
ounces (fl oz). What is the volume of the
can in quarts? (Given: 1 qt = 32 fl oz)
Dimensional Analysis
(Factor-Unit Method)
• Example: Solution
– A can of Coca-Cola contains 12 fluid
ounces (fl oz). What is the volume of the
can in quarts? (Given: 1 qt = 32 fl oz)
12 fl oz  CF  ______ pounds
Dimensional Analysis
(Factor-Unit Method)
• Example: Solution
– A can of Coca-Cola contains 12 fluid
ounces (fl oz). What is the volume of the
can in quarts? (Given: 1 qt = 32 fl oz)
12 fl oz  CF  ______ pounds
1 quart = 32 fl oz
Dimensional Analysis
(Factor-Unit Method)
• Example: Solution
– A can of Coca-Cola contains 12 fluid
ounces (fl oz). What is the volume of the
can in quarts? (Given: 1 qt = 32 fl oz)
1 quart
12 fl oz 
 ______ quarts
32 fl oz
1 quart
32 fl oz
32 fl oz
1 quart
Dimensional Analysis
(Factor-Unit Method)
• Example: Solution
– A can of Coca-Cola contains 12 fluid
ounces (fl oz). What is the volume of the
can in quarts? (Given: 1 qt = 32 fl oz)
1 quart
12 fl oz 
 0.38 quarts
32 fl oz