Dimensional Analysis

We use dimensional analysis as a fail proof process to convert from one unit to another.

Unit Conversions

Unit conversions deal with three basic areas of measurement: length, volume and mass

Example: Every Saturday morning Gregor has to travel from Main Campus to his parents’ home. If his car gets 58.5 km/L how many L will his car need to travel the 19.3 miles?


Set up the problem to begin with your given information and to end with your unknown information. 

Example: A backyard swimming pool holds 315 cubic yards (yd3) of water. What is the mass of the water in pounds?


Example: An intravenous bag delivers medication to a patient at a rate of 2.75 drops a second. If a drop weighs 42 mg, how many grams of solution are delivered in 7.0 hours?


Understanding Dimensional Analysis

Dimensional Analysis is just simply a word problem dealing with unit conversions. It is design to begin with your given value and to end with the unknown value we need to find. 

Example: Natty Light contains 4.2% alcohol. Steve from Kappa Epsilon Gamma, KEG for short, wants to get tanked tonight, and he is aiming to down at least 175 ml of alcohol in one night. If each can of Natty light contains 355 mL of beer, how many cans of Natty Light must Steve consume at minimum to reach his goal? 


Example: A Volkswagen diesel engine consumes diesel at a rate of 25.83 L per hour. If the density of the diesel is 0.850 g/mL, what is the mass (in mg) of diesel needed to drive for a continuous 8.5 hours? 


Example: An acetaminophen suspension for toddlers contains 95 mg/0.85 mL suspension. The recommended dose is 22 mg/kg body weight. How many liters of this suspension should be given to a toddler weighing 30.5 lbs?


Dimensional Analysis & Density

Density establishes a relationship between mass and volume. 

Example: If the density of an unknown metal is 21.4 g/cm3, express its density in lb/ft3.  Remember that 1 in = 2.54 cm.


Density questions can include dimensional analysis so remember to use the same approach as you would normally. 

Example: A piece of unknown metal weighs approximately 0.45 lbs. When a scientist places it in a glass beaker the water level increases from 1.85 L to 2.13 L. What is the density of the palladium metal in g/mL? 


In a water displacement question the volume of the water increases with the added volume of the unknown substance. 

Example: The U.S. Environmental Protection Agency sets the maximum safe level of lead in blood at 24 μg per dL of blood. The average person has 60 mL of blood per kilogram of body weight. For a 63.7-kg (140.459 lb) person, what is the total maximum safe content of lead in blood?