The Factor Label Method of unit conversions:
Start with this problem:
7 x 17 =
5 7
Did you see that you can cancel out the two 7’s to simplify the problem?
7 x 17 = 17
5 7
5
This is the basis of the Factor Label method, which we will use in chemistry to help us keep
organized as we do difficult problems.
Memorize this simple poem to remember the steps of Factor Label:
Write the statement first.
Next find conversion factors. Set them up bottom unit first.
Let’s use Factor Label to answer the following question: How many centimeters are in 32
feet?
1. Write the statement first.
That’s what you are starting with. In this case, it is 32 feet.
2.
Next find conversion factors. Set them up bottom unit first.
Now you need to find conversion factors, or fractions that will help you find your answer.
Your statement says 32 ft
How can you get from feet to centimeters? Look at your reference sheet. You can go from feet to
inches, and then from inches to centimeters. Write each conversion factor so the unit will cancel
out (like you cancelled the 7 out in the first problem above). Look at the example below. Does feet
cancel? Do inches cancel?
32 ft x 12 inches x 2.54 cm =
1 ft
1 inch
Once you have the set up, you’re ready to do the math. Cancel out the units – if you’ve done it right,
they should all cancel. Then multiply (and divide, if necessary) to get your answer.
32 ft x 12 inches x 2.54 cm = 32 x 12 x 2.54 = 975.36 cm
1 ft
1 inch
So 32 ft = 975.36 cm.
A couple of comments:
Each and every conversion factor should equal the number one. For example, if 1 inch = 2.54 cm,
then 1 inch = 1
2.54 cm
I don’t like factor label. I would rather use proportions!
Factor label is a short cut based on proportions. It’s actually easier than proportions once you get
used to it.
For example, suppose you want to convert 44.5 inches to cm. Set up the proportion:
x cm = 2.54 cm
44.5 in
1 inch
Cross multiply:
(x cm) (1 inch) = 44.5 inch x 2.54 cm
Solve for x:
X = 44.5 inch x 2.54 cm = 113.03 cm
1 inch
Compare: in factor label we would write
44.5 in x 2.54 cm = 113.03 cm
1 inch
Factor label is proportions, just starting halfway through.
Later on in chemistry, factor label is great for longer problems such as
Factor Label and Fractions
EXAMPLE: Convert 4.5 m/s to miles per hour. Follow the factor label method, only you’ll have to
do top units first for the seconds. Study the example below.
4.5 m
1 sec
x
60 seconds x 60 minutes x 1 km x
1 minute
1 hour
1000 m
1 mile =
1.6093 km
Factor Label and cubing (or squaring, etc)
EXAMPLE: convert 6.5 m3 to cm3. Each conversion factor will need to be cubed.