Name___________________
Teacher__________________
Dimensional Analysis in Three Simple Steps
You can use the following three-step process to convert any given unit to the unit you need:

Write a conversion factor that relates the given unit to the wanted unit. If you cannot
relate the two units directly with a single conversion factor, write a conversion factor
that relates the given unit to an intermediate unit.

Multiply the given unit by the conversion factor from Step 1. Follow the algebraic rules
from multiplication of fractions.

If the result of Step 2 is the wanted unit, the conversion is finished. If not, you must
convert the intermediate unit. If another conversion is necessary, repeat Steps 1 and 2
until you arrive at the wanted unit.
Example#1:
Convert 45.3 cm to its equivalent measurement in mm.
Solution:
Select a conversion factor which will convert the unit "cm" to the unit
"mm". The appropriate conversion factor is: 10 mm / 1 cm. Arrange
the problem so that the given measurement, when multiplied by the
correct unit factor, will yield an answer with the proper label:
45.3 cm X 10 mm = 453 mm
1 cm
Here is an example of a conversion that requires two steps:
Convert 3.00 feet to centimeters given 1 foot = 12 inches and 1 inch = 2.54 centimeters.
3.00 ft x 12 in./ft x 2.54 cm/in. = 91.4 cm
Practice Questions:
1. Use the dimensional analysis (unit conversion, factor label) problem-solving method to answer the
following questions.
a. How many nickels would you get for a twenty dollar bill?
20 dollar bill= 20 loonies
1 loonie= 4 quarters
1 quarter = 5 nickles
b.
How many hours are in a week?
24 hours=1day
7 days=1week
2.
Calculate the number of seconds in a year.
60 seconds= 1 minute
60 minutes= 1 hour
24 hours=1 day
365 days= 1 year
3. The units of the chain system of measure, used by surveyors, are as follows:
7.92 inches = 1 link
100 links = 1 chain
10 chains = 1 furlong
80 chains = 1 mile
The distance of the Kentucky Derby, a classic horse race, is 1.25 miles. How is this distance expressed in
furlongs?