# Homework Help: Finding errors

1. Apr 2, 2010

### lemon

1. The problem statement, all variables and given/known data
$$$\[ \begin{array}{l} {\rm{A quantity Y is given by:}} \\ Y = \frac{{4a^3 b}}{{\left( {5c^2 \sqrt {\rm{d}} } \right)}} \\ {\rm{Find the error in Y given the following errors in a, b, c, and d:}} \\ a \pm 1\% ,{\rm{ }}b \pm 0.5\% ,{\rm{ }}c \pm 2\% ,\,{\rm{ }}d \pm 1.5\% \\ \end{array}$ \$$

2. Relevant equations
Given above

3. The attempt at a solution
I plugged the numbers into this equation and got 0.1632993162
This is not correct.
I added all the percentage errors together to get 5%. Then asked myself why I did that anyway.
Don't know how to solve this problem. I know how to find percentage errors but these are already given.

And also - My LaTex is not working properly - It doesn't recognize the spaces between the words from MathType. Anyone know why?

Last edited: Apr 2, 2010
2. Apr 2, 2010

### Stonebridge

When you combine errors in a formula containing powers with the terms multiplied and divided you add the percentage errors of all the terms, but with the additional factor that if a term is squared the % error is doubled, if it's cubed the % error is 3 times. etc etc.
You can probably find a proof of this online.

3. Apr 17, 2010

Thank you