Dimensional Analysis
 Dimension = unit
 Analyze = solve
 Using the units to solve the problems.
Dimensional Analysis
The “Factor-Label” Method
 Units, or “labels” are canceled, or
“factored” out
g
cm 

g
3
cm
3
Dimensional Analysis
Steps:
1. Identify starting & ending units.
2. Line up conversion factors so units
cancel to give the desired unit for the
answer.
3. Multiply all top numbers & divide by
each bottom number.
4. Check units & answer.
Dimensional Analysis
 Lining up conversion factors:
1 m = 100 cm
=1
100 cm 100 cm
1 m = 100 cm
1=
1m
1m
Dimensional Analysis
A rattlesnake is 2.44 m long. How long is
the snake in cm?
m
cm
2.44 m
100 cm
1m

= 244 cm
How many minutes are in 2.5 hours?
Initial unit
hr
Conversion
factor
2.5 hr
x 60 min
final unit
min
= 150 min
1 hr
Answer (2 SF)
cancel
Learning Check
How many seconds are in 1.4 days?
Unit plan: days
hr
min
seconds
2 SF
Exact
1.4 days x 24 hr x 60 min x 60 sec
1 day
1 hr
1 min
= 1.2 x 105 sec
Unit Check
What is wrong with the following setup?
1.4 days
x 1 day
24 hr
x
60 min
1 hr
x 60 sec
1 min
Unit Check
1.4 days
x 1 day
24 hr
x
Units = day2 sec
hr2
Not the final unit needed
60 min
1 hr
x 60 sec
1 min
Dimensional Analysis
 Lining up conversion factors:
1 in = 2.54 cm
=1
2.54 cm 2.54 cm
1 in = 2.54 cm
1=
1 in
1 in
Dimensional Analysis
Your European hairdresser wants to cut
your hair 8.0 cm shorter. How many
inches will he be cutting off?
cm
in
8.0 cm 1 in
2.54 cm

= 3.2 in
Dimensional Analysis
13 inches is how many yards?
(36 inches = 1 yard)
in
yd
13 in
1 yd
36 in

= 0.36 yd
Dimensional Analysis
 How many milliliters are in 1.00 quart of
milk? (1.057 qt = 1 L)
qt
mL
1.00 qt

1L
1000 mL
1.057 qt
1L
= 946 mL
Dimensional Analysis
Taft football needs 550 cm for a 1st down.
How many yards is this?
cm
550 cm
yd
1 in
1 ft 1 yd
2.54 cm 12 in 3 ft
= 6.0 yd
Learning Check
An adult human has 4650 mL of blood. How many
gallons of blood is that?
Equalities:
946 mL = 1 quart
4 quarts = 1 gallon
Unit plan:
mL
4650 mL
3 SF
x
qt
1 qt__ x
946 mL
exact
gallon
1 gal_
= 1.23 gal
4 qt
3 SF
Learning Check
If the ski pole is 3.0 feet in length, how long is
the ski pole in mm?
3.0 ft x 12 in
1 ft
x 2.54 cm x 10 mm = 910 mm
1 in.
1 cm
Dimensional Analysis
1. A ruler is 12.0 inches long. How long is it in
cm? in meters? (1 inch is 2.54 cm)
2. A race is 10.0 km long. How far is this in
miles?
 1 mile = 1760 yd; 1 meter = 1.094 yd
3. Pikes peak is 14,110 ft above sea level.
What is this in meters?