We use dimensional analysis as a fail proof process to convert from one unit to another.
Concept #1: Understanding Unit Conversions
Unit conversions deal with three basic areas of measurement: length, volume and mass.
Example #1: 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 #2: A backyard swimming pool holds 315 cubic yards (yd3) of water. What is the mass of the water in pounds?
Practice: 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?
Concept #2: Examining Dimensional Analysis
Dimensional Analysis is 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 #3: 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 #4: 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?
Practice: 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?