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This is a problem from a book i'm reading. The $ \pm\frac{1}{400}$ and $\mp\frac{16}{400}$ represent tolerances of some quantities and i'm looking to find the total tolerance/sensitivity in the quantity $n$.

So i'm confused here. The book gives the answer as $\pm4.25\%$ which means that he performed the calculation: $\pm\frac{1}{400} \pm\frac{16}{400}=\pm\frac{17}{400}=\pm4.25\%$. Why? I personally interpret the opposite plus-minus symbols as a subtraction, which is why i found $\mp\frac{15}{100}$(which should be equal with: $\pm\frac{15}{400} = 3.75\%$). Which one is right and why?

And another question. In general, i'm wondering how should one go about to solve an equation such as this. Should we:

a) first take the positive of $\pm\frac{1}{400}=\frac{1}{400}$ and then take cases for both plus and minus of $\frac{16}{400}$ and then the negative, which totals 4 solutions. ?

Or

b) find 2 solutions, according to the operations as shown. I mean to find those two solutions: $1)\ n=\frac{1}{400} -\frac{16}{400} $ and $2)\ n=-\frac{1}{400} +\frac{16}{400} $ ?

Thanks in advance.

KeyC0de
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1 Answers1

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The $\pm$ and $\mp$ signs are kind of ambiguous in general; sometimes the right thing to do is a) and sometimes it's b). The context you're working in should make it clear (which isn't to say that it always does, but if it doesn't then you need to step back and think carefully about what's going on).

In your specific case, you're looking at tolerances, which means that a) is probably the right option. The expressions $\pm \frac{1}{400}$ and $\mp \frac{16}{400}$ presumably represent different sources of error in your measured quantity. As a general rule, there's no reason to assume that the error from one source should have anything to do with the error from the other source. If you just subtracted one from the other you'd be assuming that you got lucky, and your errors from the two sources were likely to balance each other out.

Option b) would be more appropriate for more algebraic/exact uses of the $\pm$ sign (like in the quadratic formula).

Micah
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  • Thanks for answering. This is the first time i see something in math that's ambiguous. In "Mathematics" where everything should be unambiguous and precise. Yes, in my example (my first question), we assume that the two variables that gave me those different tolerances ($\pm \frac{1}{400}$ and $\mp\frac{16}{400}$) are uncorrelated. Again in the first question i subtracted getting $\mp \frac{15}{400}$ because this seemed more logical to me. And finally (by thinking carefully) $\mp\frac{15}{400} = \pm\frac{15}{400}$ because both represent the same tolerance. – KeyC0de Sep 27 '15 at 16:06