# Guilty of order-of-magnitude neglect

I’ve often commented on the failure of students to apply common sense when calculating physical quantitites. For example, perhaps I ask them to calculate or estimate the pressure exerted by a car tyre on the road (with the car attached to the tyre) and they punch their figures into a calculator and get 10.4 pascals. (For those that aren’t familiar with the physics needed here, just note that ten pascals is WAY too low – for example, atmospheric pressure is about 100 kilo (thousand) pascals.)

What’s happened is that the students have made a mistake somewhere – perhaps they’ve hit ‘divide’ rather than ‘multiply’ on their calculator, or neglected to account for ‘mega’ meaning ‘a million’. That happens occasionally and is excusable. What isn’t excusable is when the incorrect answer is written down without a thought towards common sense. Just a tiny bit of thought will tell a physicist that the pressure exerted is much higher than 10 pascals, which is what you’d get by spreading out a kilogram mass of something over a metre sqaured of surface. An experienced physicist such as myself would never make such a blunder.

Well…except…Umm…maybe…just occasionally. Currently, my church (not MY church, but you know what I mean) is considering various renovations, and I’ve been involved with looking at the options and prices etc. One of the things we’d like to do is to remove the pews and replace them with nice, new, comfortable chairs. The chairs that our pastor is eyeing up are 80 dollars each – when you multiply that by two-hundred-and-something we get a total price of about 18 thousand dollars. It ain’t cheap. Anyway, on Monday night I was putting together some powerpoint slides for the congregation on the renovation and how to fund it, etc, and, with the numbers, eighty, eighteen, and thousand sloshing around in my head I wrote down $80k as the price it would be. Understandable, maybe, to make that mistake (particularly after a hard day at work doing general administrative stuff), but not excusable to write it down without thinking. Eighty thousand dollars for some chairs is just a little steep. Fortunately I sent my slides to some others for checking first, before it resulted in major embarrassment.

## One Response to “Guilty of order-of-magnitude neglect”

One typical mistake (and it is very simple) that I find some high school students in physics that I coach in the evening is not converting the units into SI. If a problem where the distance is given in kilometers and acceleration is given in meters/sec^2 and the velocity of the object is required to be calculated, where the object starts from rest, they just plug in the numbers given without converting them into SI units first. When they check the answer at the back of the textbook, they’re often puzzled why their answers are incorrect, even they’re using the correct formulas. The other thing that might have missed them completely is that the hint is given in the answer’s units. If they had pay attention to the units in the answer, then they would have realized that they should have to convert everything into SI before substituting them into the formula.

Not converting into SI units so everything is the same but using the figures given directly, will lead to too small answer or too big answer. Even with some common sense when one looked at the answer and noted that it is too big or too small, and yet it still doesn’t even register with them that there might be something wrong.