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Two lengths are (15.6 ± 0.2) cm and (9.1 ± 0.1) cm.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Two lengths are $(15.6 \pm 0.2)\ \text{cm}$ and $(9.1 \pm 0.1)\ \text{cm}$ . Find their sum and their difference, each with its error and percentage error.

Need a reminder? The key ideaShow

For a sum or a difference, the absolute errors add. For a product or a quotient, the relative errors add, each multiplied by its power:

\displaystyle Z = \frac{A^p B^q}{C^r} \;\Rightarrow\; \frac{\Delta Z}{Z} = p\frac{\Delta A}{A} + q\frac{\Delta B}{B} + r\frac{\Delta C}{C}

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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