Exams are looming, and I’ve had a constant stream of students coming to me this week asking me questions.
One question I’ve had has been asked by two students independently, relating to an example calculation done in a text book. The question goes like this: "I’ve been going through this example, and I get the answer 0.159, but the book says its 160. I don’t get it"
To be honest, I’m a bit saddened that students weren’t able to figure this one out for themselves. Experience tells me that when I am a factor of 1000 out, it’s almost always because of an issue with the units – somewhere a ‘milli-something’ or a "kilo-something" has been overlooked. It is what comes from extracting numbers from a question and putting them into the calculator without thinking about what numbers are being used. And, indeed, if the students had looked at the units the textbook answer was given in, they would have spotted that the book’s 160 mA m-1 is exactly the same as the 0.159 A m-1 the student has. (Here also we have a significant figures issue).
The students’ question says it all.."I get the answer 0.159". But 0.159 what?
Units and dimensions are fundamentally key to physics. There’s probably no other area where they are so critical. One could even say that units is what physics is all about. Describing physical quantities. Units are so important that there is a whole area of branch of physics devoted to establishing them in practical terms – metrology – and international committees dedicated to doing such boring (but essential) things as deciding on what one ampere actually means. Without this, physics will fall apart. This is one reason why lecturers like me bleat on about paying attention to the units.