Dimensional Analysis
Part I.
Simple Unit
conversion
Dimensional Analysis I.
Simple Unit Conversion

Typical problem:
I have 5.3 lbs of Aluminum(Al), how
many grams of Al is this?
I have 5.3 lbs of Al, how
many grams of Al is this?
Steps to solve:
1. Identify starting units.
2. Identify ending units.
3. Identify a unit conversion factor(s) that
connect starting and ending units.
(You may need more than one.)
4. Arrange the conversion factors in an equation
so that they cancel the starting units and
leave only the final unit. (No calculation)
5. Plug in the numbers and solve the equation.
I have 5.3 lbs of Al, how
many grams of Al is this?

Step 1. Identify starting units
Lbs (pounds)
I have 5.3 lbs of Al, how
many grams of Al is this?

Step 2. Identify ending units
g (grams)
I have 5.3 lbs of Al, how
many grams of Al is this?

Step 3. Identify unit conversion factor that connects
starting and ending units (you may need more than one)
Start
lbs (pounds)
End
g (grams)
Look at conversion table (Appendix 6, page A27 of your text)
Locate section on mass
3 conversions look useful
1 kilogram = 2.2046 pounds
1 pound = 453.59 grams
1 pound = 0.45359 kilograms
I have 5.3 lbs of Al, how
many grams of Al is this?
Step 3. (continued)
Start
End
lbs (pounds)
g (grams)
3 conversions look useful
1 kilogram = 2.2046 pounds
1 pound = 453.59 grams
1 pound = 0.45359 kilogram

The second conversion factor is the one we want
because it exactly matches the units in our
problem, grams and pounds
I have 5.3 lbs of Al, how
many grams of Al is this?
You now have a conversion equation:
1 lbs = 453.59 g
You can arrange this equation as a conversion
factor in two different ways
1.0 lbs/453.59 g
-or-
453.59 g/1.0 lbs
I have 5.3 lbs of Al, how
many grams of Al is this?

Step 4. Arrange conversion factor in an equation so it
cancels the starting unit and changes it to the final unit
(No numbers)
Which one will cancel starting units and change to final
units?
Lbs = g
Lbs x (g/lbs) = g
Right !!
Lbs x (lbs/g) = (lbs · lbs)/g
Wrong!
I have 5.3 lbs of Al, how
many grams of Al is this?

Step 5. Put in the numbers and solve the
equation
Start x conversion factor = Final
Lbs x (g/lbs) = g
5.3 lbs x (4.5359 g/ 1 lbs) = g
= 2404 g
=2400 g with sig fig!
Dimensional analysis
Practice problems

On the next few pages I have some
practice problems for you. Do each
step on your own, see if you get the
answer correct. Use the conversion
tables in Appendix Six of your text.
I just ran 0.25 miles, what
is this in kilometers?
Step 1: Starting units ?
Mile
Step 2: Ending units ?
kilometers
Step 3: Conversion factor?
1 mile = 1.6093 kilometers
Step 4: Equation?
Mile x (kilometer/mile)
Step 5: Solve
0.25 mile x (1.6093 km/1 mile) = .4023 km
=.40 km with sig fig
The gas tank of my car holds 14
gallons. How many liters is this?
Step 1: Starting units?
gallons
Step 2: Ending units?
liters
Step 3: Conversion factor?
1 gallon = 3.7854 liters
Step 4: Equation?
Gallons x (liters/gallons)
Step 5: Solve:
14 gallons x (3.7854 liters/1 gallon)=52.99
liters
=52 liters with sig fig
This morning I swam 1000.
meters, how many yards is this?
Step 1: Starting units
meters
Step 2: Ending units
yards
Step 3: Conversion factor
1 meter= 1.0936 yards
Step 4: Equation
meters x (yards/meter)
Step 5: Solve
1000. meters x (1.0936yard/meter)
=1093.6 yards
=1094 yards with sig fig
The pressure in Spearfish is 734 torr.
What is this in Atmosphere (atm)?
Step 1: Starting units
torr
Step 2: Ending units
atm (Atmosphere)
Step 3: Conversion factor
1 atmosphere= 760 torr
Step 4: Equation
torr x (atm/torr)
Step 5: Solve
734 torr x (1 atm/760 torr)=0.966 atm
=.996 atm with sig fig