# Finding errors

lemon

## Homework Statement

$$$\[ \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}$ \$$

Given above

## 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?

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## Answers and Replies

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.

lemon
Thank you