# Explain my mathematical failure

I was helping someone earlier today with their GCSE Physics revision (international dopers might get an idea of the level of study from this Wikipedia article). Most of the help was explaining how the examiners awarded full marks for a question, i.e. show all necessary working out and not just the answer alone.

One question however, stumped me, with my working out falling short as well as the answer itself; a current of 2500 amps runs for 1 millisecond, what was the electrical charge over this time? OK thought I, Charge (Q) = current (I) x time (t), so the charge is 2500 x 1/1000 = 2.5 C.

I missed out on full marks however. According to the marking papers, I should have calculated a charge of 2500 mC, calculated by multiplying 2500 x 1. The marking papers showed my method was marked down because of a “10 to the power of n” error.

I’m not sure what the difference is or what this power of n error means. I’d appreciate if someone could break it down for me so I could explain to the student.

Your answer and methods seem perfectly fine to me, with one caveat. I think the confusion is because when you wrote “2500 x 1/1000 = 2.5 C”, it was unclear that what you really meant was “2500 amps x 1/1000 seconds = 2.5 C”. If you had instead meant “2500 amps x 1/1000 milliseconds = 2.5 C”, then there would be some power of ten errors, in the sense that this latter equation is not true, the left hand side being a thousandth of the right hand side, and 1/1000 milliseconds being a thousandth of the actual quantity of interest, 1 millisecond (equivalently, as you realized, 1/1000 second).

So, the only caveat I would give is that you should have explicitly written the units you were using to stave off this ambiguity (since, after all, the problem was stated using the units of milliseconds, one might have assumed you as well were using milliseconds initially, rather than seconds).

And, of course, as I’m sure you realize, 2.5 C = 2500 mC. The reason they gave their answer in mC is because 1 amp * 1 millisecond = 1 mC, and they simply stayed with milliseconds and millicoulombs instead of switching to seconds and coulombs. But your answer is equivalent and thus also correct.

2.5 C = 2500 mC. Your answer was correct; marking it as incorrect was an error.

ETA: I’m assuming you showed your units correctly on the actual paper; i.e. 2500 A * (1/1000) s = 2.5 C. If you put (1/1000) ms or something, yeah, that’d be wrong.

I’m not really sure - other than some supposed requirement of the examiner to give the result in milliCoulombs because the time was given in milliseconds?

2.5C is the same as 2500mC, so your answer is correct, it’s just 10^3 smaller because you specified C as your unit, which is perfectly fine in my opinion.

But as someone who never saw eye to eye with the ludicrously arbitrary nature of GCSE mark schemes - you’ll see pedantry like that lose marks, but somehow it’s fine that pi = 3 and G = 10.

Madness. Everyone knows pi is exactly 22/7.

Does that actually happen? I know when I took AP exams in high school, specifically for AP physics, they’d accept equivalent answers. 2.5 C or 2500 mC or 2500000 µC or 25 dC or whatever I damn well felt like putting down, as long as it was correct. Seems bizarre that marking an equivalent answer incorrect would be a matter of policy, especially given that there is no rule on which prefix is canonical for use in a given problem.

I am very much afraid that you lost out to a fatuous examiner. Unless they specified that the answer be in microcoulombs, you cannot take exception to the answer. I recall being startled by one student who came up with a completely unexpected solution to a question that involved considerably less work than the solution they had been shown. Not only did she get full marks, but a commendation.

I wonder if that could be it, I’ll double check the marking sheet again.

I wonder if this could be some misapplication of significant figures (on the test scorer’s part, not yours). It’s not really typical on a Physics exam to worry about the provenance of your data, though. But that could have been the principle they were trying to apply. Unfortunately they might completely misunderstand how it works and think that “maintaining the prefixes” is somehow a rule that should be promoted in general.

It means you were off by 10^1 or 10^2 or 10^3, etc.

I think Indistinguishable is on the right track. ALWAYS SHOW YOUR UNITS!