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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.
Convert 45.3 cm to its equivalent measurement in mm.
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
How many hours are in a week?
24 hours=1day
7 days=1week
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