I have done similar questions but this one does not give a value for r. Should I give it any value?

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- Aug 7th 2010, 04:06 AMStuck ManAccuracy question
I have done similar questions but this one does not give a value for r. Should I give it any value?

- Aug 7th 2010, 04:55 AMArchie Meade
No need...

$\displaystyle relative\ error=\frac{absolute\ error}{exact\ value\ of\ that\ being\ measured}$

$\displaystyle =\displaystyle\huge\frac{{\pi}r^2-{\pi}\left(r-\frac{r}{400}\right)^2}{{\pi}r^2}=\frac{{\pi}r^2-{\pi}r^2\left(1-\frac{1}{400}\right)^2}{{\pi}r^2}$

or

$\displaystyle \displaystyle\huge\frac{{\pi}\left(r+\frac{r}{400} \right)^2-{\pi}r^2}{{\pi}r^2}=\frac{{\pi}r^2\left(1+\frac{1} {400}\right)^2-{\pi}r^2}{{\pi}r^2}$

which may be factorised, removing $\displaystyle r$ and $\displaystyle \pi}$ completely.

Those parameters are needed for the "absolute" error,

but not for the "relative" error. - Aug 7th 2010, 05:03 AMStuck Man
Ok. In general is the absolute error either +ve or -ve? Is an error bound always positive? Wikipedia seems to muddle these things up.

- Aug 7th 2010, 05:38 AMArchie Meade
- Aug 7th 2010, 06:13 AMStuck Man
To calculate the absolute error you've taken the minimum value of r so you must also take the minimum value of pi which is 3.1415. This will get the answer in the book. Part b is done similarly for pi=3.14159.

- Aug 7th 2010, 06:21 AMStuck Man
There is much more work than this. I know how to do it though.