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For my latest maths PSMT, the teacher has specified that equals signs should only be used if the values are actually equal. Does that mean I should use an approximation sign if I'm rounding the values to two decimal places?

This is what I've been doing so far...

\begin{align} &x = -5.057588.... \\ &x = -5.06\;\text{(2 d. p.)} \\ \end{align}

Should I be using an approximation sign instead? Should I remove the $\text{(2 d. p.)}$ at the end?

blackjack_sparrow
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2 Answers2

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I would rather use $$x=−5.057588\ldots \\ x\approx -5.06$$ since they are not exactly equal. I Agree with your teacher.

Arroz con Tomate
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    I would even go so far as to use $x \approx −5.057588 \ldots$ as well, since that is also an approximation. The equals sign is for when results are equal, or when you're in elementary school and things are simpler. – Prime Mover Mar 08 '21 at 08:33
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If you intend to be strictly precise, then :

\begin{align} &x \approx -5.057588.... \\ &x \approx -5.06\;\text{(2 d. p.)} \\ \end{align}

because at base those numbers are only ever approximations.

On the other hand, saying "$x$ is equal to $-5.06$ correct to $3$ significant figures" could be interpreted as needing an equals sign, so I believe either could be used here. I anticipate disagreement with other contributors as to which is strictly correct, either $x = -5.06 \ \text {(to $3$ s.f.)}$ or $x \approx -5.06 \ \text {(to $3$ s.f.)}$

Also please note that there are purists who say that "$\text {(to $2$ d.p.)}$" presupposes that you do not round the last place, but that it should be "$x \approx -5.05 \ \text {(to $2$ d.p.)}$" because you are quoting the decimal places, not the significant figures of accuracy.

Hence it may be a good habit to get into to prefer the use of significant figures when discussing the precision and/or accuracy of a number, and not decimal places. The former is more general and is unchanged when changing the units of measurement: $5.06 \, \mathrm {cm} \ \text {(to $3$ s.f.)}$ is the same thing as $50.6 \, \mathrm {mm} \ \text {(to $3$ s.f.)}$ is the same thing as $0.00506 \, \mathrm {m} \ \text {(to $3$ s.f.)}$, but you can't say the same about the decimal places.

However, it all depends on whether you are using mathematics as a professional in an engineering field, or whether you are merely using it to teach schoolchildren. I believe the goals are different.

Prime Mover
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