How to calculate uncertainties? A question requires me to make a calculation involving variables with uncertainties, giving my answer with its result uncertainty.
How do I do that?
 A: Firstly, you should understand fractional uncertainty
$= \frac{\Delta x}x$ and percentage uncertainty $= \frac{\Delta x}x \times 100$  
Also be careful where you are given a length with its uncertainty and required to calculate, for example, density of a cube. The volume of the cube is the length$^3$, and so the power rule applies (see below). 
Now for some examples:  


*

*Addition/Subtraction.
$x = a \pm \Delta a$
$y = b \pm \Delta b$
$x + y = (a + b) \pm (\Delta a + \Delta b)$
$x - y = (a-b) \pm (\Delta a + \Delta b)$  

*Multiplication & Power rule.
$x = abc^2$
$\Delta x = \pm \left[ \frac{\Delta a}a + \frac{\Delta b}b + 2\frac{\Delta c}c \right]\cdot abc$  

*Division & Power rule.
$x = \frac{ab}{c^2}$
$\Delta x = \pm \left[ \frac{\Delta a}a + \frac{\Delta b}b + 2\frac{\Delta c}c \right]\cdot \frac{ab}{c^2}$  

*$\log$ / $\ln$
$T = x \pm \Delta x$
$\log T = \log x \pm \Delta \log T$
$\Delta \log T = \pm \left[ \log (x + \Delta x) - \log x \right]$  


Leave the result uncertainty to the same number of significant figures as the given uncertainty.
Measures you should know:
\begin{align}
10^{12} & = \text{Tera (T)} \\
10^9 & = \text{Giga (G)} \\
10^6 & = \text{Mega (M)} \\
10^3 & = \text{kilo (k)} \\
10^{-1} & = \text{deci (d)} \\
10^{-2} & = \text{centi (c)} \\
10^{-3} & = \text{milli (m)} \\
10^{-6} & = \text{micro ($\mu$)} \\
10^{-9} & = \text{nano (n)} \\
10^{-12} & = \text{pico (p)}
\end{align}
