Accuracy question

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August 7th 2010, 05:06 AM
Stuck Man

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Accuracy question

I have done similar questions but this one does not give a value for r. Should I give it any value?
August 7th 2010, 05:55 AM
Archie Meade

Quote:

Originally Posted by Stuck Man

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

No need...

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

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

or

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

which may be factorised, removing $r$ and $\pi}$ completely.
Those parameters are needed for the "absolute" error,
but not for the "relative" error.
August 7th 2010, 06:03 AM
Stuck 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.
August 7th 2010, 06:38 AM
Archie Meade

Quote:

Originally Posted by Stuck 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.

It would be positive,
however that's because the modulus is taken,
which doesn't mean we get the same error here if the radius is lower by 0.25%
or if it's higher by 0.25% from it's nominal value.
August 7th 2010, 07:13 AM
Stuck 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.
August 7th 2010, 07:21 AM
Stuck Man

There is much more work than this. I know how to do it though.