Dimensional Analysis

Using the Conversion Factor
Objective: Make unit conversions
Unit conversion factor
A unit conversion factor is a fraction whose
numerator and denominator are equivalent
measures. Some common unit conversion factors
are given below. You can also use the reciprocal of
these.
Choose a unit conversion factor
that…
• Introduces the unit you want in the
answer
• Cancels out the original unit so that
the one you want is all that is left.
IN ORDER FOR UNITS TO CANCEL,
THEY MUST BE DIAGONAL
“Canceling” out Words
inches feet

feet
miles
inches

miles
seconds hours
hours


minutes seconds
minutes
Practice: Choose the appropriate
conversion factor.
Inches to feet
Minutes to hours
Meters to centimeters
inches
1
1 ft
12 in.
minutes
1
60 min
1 hr
meters
1
1m
100 cm
12 in.
1 ft
1 hr
60 min
100 cm
1m
inches needs to be on the bottom (DIAGONAL) to cancel
minutes needs to be on the bottom (DIAGONAL) to cancel
meters needs to be on the bottom (DIAGONAL) to cancel
Convert 8 yards to feet…
Make a decision: What conversion factor will you use?
8 yards
1
3 ft
1 yd
or
1 yd
3 ft
Set up the problem: Multiply the measurement by the
conversion factor.
3 ft
8 yd 
1 yd
Solve the problem: Perform the multiplication
= 24 ft
A bucket holds 16 quarts. How many gallons of
water will fill the bucket? Use a unit conversion
factor to convert the units.
What are the two conversion
factors comparing quarts and
gallons?
4 qt
1 gal
Which one will “cancel”
quarts?
16 qt 
= 4 gal
1 gal
4 qt
One bag of apples weighs 64 ounces. How many pounds does it
weigh?
= 4 lbs
Darren drank 2 liters of water. How many milliliters of water did
he drink?
= 2000 mL
Convert 80 miles per hour to feet per sec.
= 117 ft/s
Convert 3 x 108 m/s to miles per hour.
= 6.71 x 108 mph
Convert 32 feet per min to inches per second.
= 6.4 in/s
A craft store charges $1.75 per foot for lace. How much per yard
is this?
= $ 5.25 per yard
Recall : 1 mol = 6.02 x 1023 atoms
1 mol of argon occupies 22.4 L
How many Argon atoms are in 8170 mL?
2.196 x 1024 Ar atoms