# Small question about accuracy and precision

Let's say I have a law like this, $$D=\frac{c}{r}$$ where $c$ is a constant, $r$ a distance in meter. my measures of $r$ are [$0.02m$, $0.01m$], then $<r>=0.015m$ and $\delta r = \pm 0.005m$. So now if I want to calculate $D+\delta D$ should I use $+\delta r$ or $- \delta r$ in my equation?

because if I use $+\delta r$ I get a smaller value than if I use $-\delta r$ since $r$ divide $c$

edit: in my real problem I have a lot of data, all is fine when I use the minus delta. I just want to be sure...

• You may be interested in the LaTeX commands \langle and \rangle to produce $\langle r\rangle$, and the proper way $1\:\mathrm{m}$ to produce $1\:\mathrm{m}$. – Emilio Pisanty Apr 4 '14 at 21:29
• @EmilioPisanty thx for that comment – The Unholy Metal Machine Apr 4 '14 at 21:38

The standard way to propagate uncertainties is, in this case, $$\delta D = \left|\frac{\partial D}{\partial r}\right|\delta r=\frac{c\, \delta r}{r^2},$$ where $\delta r$ is a positive quantity. Then $\delta D>0$ gives you half the width of your uncertainty interval in $D$.