# Accuracy question

• Aug 7th 2010, 04:06 AM
Stuck Man
Accuracy 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 AM
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...

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

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

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 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.
• Aug 7th 2010, 05:38 AM
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.
• Aug 7th 2010, 06:13 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.
• Aug 7th 2010, 06:21 AM
Stuck Man
There is much more work than this. I know how to do it though.