Thread: Easy Question

When we want to find the area of a two dimensional figure and there are more than one type of shapes that can be used to find the whole figure, we find the areas of the shapes comprising the figure one step at a time. Then finally adding the areas of the shapes together to find area of the whole figure. But do we round twice or just at the end of the calculation? And does it always have to be rounded to the least number of significant figures. What does this achieve exactly? Please show an example and show your reasoning.

-Thanks

Originally Posted by Joker37

When we want to find the area of a two dimensional figure and there are more than one type of shapes that can be used to find the whole figure, we find the areas of the shapes comprising the figure one step at a time. Then finally adding the areas of the shapes together to find area of the whole figure.

Yes, this is the correct method of finding area of complex shapes. Such as a 'L' 2D shape where you would consider two rectangles.

Originally Posted by Joker37

But do we round twice or just at the end of the calculation?

We dont always round. It depends on the question.

Originally Posted by Joker37

And does it always have to be rounded to the least number of significant figures. What does this achieve exactly? Please show an example and show your reasoning.

-Thanks

^ For this shape, the area would be:

$\displaystyle (3\times4) +(5\times2) = 22\mathrm{cm}^2$

$\displaystyle 22\mathrm{cm}^2$ is the area. We did not need to round here.



^ For this shape, the area would be:

$\displaystyle (4.2\times3.2)+(5.5\times 2.7) = 28.29\mathrm{cm}^2$

$\displaystyle 28.29\mathrm{cm}^2$ is the answer and it can be kept as that (without rounding). But, if you wish to round, then you could round to 1dp as all the values were given to 1dp so the rounded area would be $\displaystyle 28.3\mathrm{cm}^2$.

It's all a matter of judgement. Personally, I wouldn't round it unless stated or if the value of the area has too many decimal places (e.g. $\displaystyle 15.89374987439732740323\mathrm{cm}^2$).

(All diagrams are not to scale)

So, just to clarify, under test conditions it wouldn't matter to which number we round it to unless it is stated in the question?

Originally Posted by Joker37

So, just to clarify, under test conditions it wouldn't matter to which number we round it to unless it is stated in the question?

In UK, under test conditions, we are asked to give the answer to 3sf unless told otherwise.

Originally Posted by Air

In UK, under test conditions, we are asked to give the answer to 3sf unless told otherwise.

But what about Australia?

Well, does anyone know? I don't want to get a zero just because I put it in the wrong the number of significant figures.

Originally Posted by Joker37

Well, does anyone know? I don't want to get a zero just because I put it in the wrong the number of significant figures.

If the writer of the exam fails to specify the accuracy to which an answer is to be given then the best you can do is to use your common sense.

In my experience this is usually only a problem with internal assessment at secondary school level. It will then depend on your teacher, not your country. Despite my personal opinion reagrding the competency of the external assessment authorities, I would be astonished if this was an issue in external examinations.

If an accuracy is prescribed then you should always use greater accuracy during the calculation than the final answer requires. Otherwise you get accumulation of rounding error and it's likely that your final answer, after rounding, won't be correct to the required accuracy. This can be a particular problem when non-trivial statistics and probability questions require answers correct to, say, 4 decimal places.


By the way: Unless the question is only worth 1 mark you will not get zero for correct working but incorrect answer.

Originally Posted by Joker37

When we want to find the area of a two dimensional figure and there are more than one type of shapes that can be used to find the whole figure, we find the areas of the shapes comprising the figure one step at a time. Then finally adding the areas of the shapes together to find area of the whole figure. But do we round twice or just at the end of the calculation? And does it always have to be rounded to the least number of significant figures. What does this achieve exactly? Please show an example and show your reasoning.

-Thanks

Very quick answer ...

In general, only round at the end. Keep as many sig.fig. as "seem sensible" in the initial workings.

Beware when subtracting one number from another that is of a similar size!