“To analyze problems dimensional,
Use method routine and conventional:
All your units bookkeep,
Lest unwanted flaw creep
Into calcs, causing steps unintentional.”
The 28 October 2019 Twitter limerick is a common exhortation in my classroom, presented here as a poetic refrain.
“To analyze problems dimensional, /
Use method routine and conventional…”
Dimensional analysis is a mathematical technique used in a variety of STEM classes. Every time I teach the practice in General Chemistry, I remind students to use a tried-and-true method– “routine and conventional”– for checking their answers.
“All your units bookkeep, /
Lest unwanted flaw creep /
Into calcs, causing steps unintentional.”
A quantity in chemistry is properly represented as both a number and the associated unit (for a simple example, “a dozen eggs” is equivalent to “12 eggs,” not simply “12”). Chemists and other scientists use “SI units,” those defined by the International System of Units, to report length (meters, or m), mass (kilograms, or kg), and other quantities; these are part of the metric system. Other systems of measurement exist; for instance, the USA uses what is known as its customary system, defining miles, feet, and inches, among many others. Different units can be converted into one another through the use of conversion factors (for instance, 1 inch = 2.54 centimeters).
Whenever students are completing chemistry-related calculations (“calcs,” for short), I repeat the importance of including units at all times, via chemical “bookkeeping.” Units can be treated algebraically and canceled out, via the steps of dimensional analysis, to ensure that calculations progress properly toward a target quantity.
I often see in grading homework that students tend to omit units until reporting their final answer, and I warn against this, as it can lead to wasted time (“steps unintentional”) or– more problematically– errors (“unwanted flaw[s]”). Infamously, mismatches in units have caused some notorious moments in STEM history, as with the loss of the Mars Climate Orbiter in 1999.
Chemphasis 