How to write it:

Uncertenties follow the form: $x\pm\Delta x\text{ unit}$

Examples: ✅ $53\pm2 \text{ cm}$ ; $(3.45\pm 0.12)10^{-9} \text{ g}$ ❌ $49\pm3.2 \text{ W}$ ; $4.010^2\pm50 \text{ AU}$

Error propagation:

• for $y=A+B \text{ or } y=A-B$:

$$ (\Delta y)^2=(\Delta A)^2+(\Delta B)^2 $$

• for $y=A*B \text{ or }y=A/B$:

$$ \left(\frac{\Delta y}{y}\right)^2=\left(\frac{\Delta A}{A}\right)^2+\left(\frac{\Delta B}{B}\right)^2 $$

• for $A=(x\pm\Delta x)+c$ {c=constant}:

$$ \Delta A=\Delta x $$

• for $A=(x\pm\Delta x)*c \text{ or }A=(x\pm\Delta x)/c$ {c=constant}:

$$ \frac{\Delta A}{A}=\frac{\Delta x}{x} $$

• for $A=c*(x\pm\Delta x)^n$ {c=constant}:

$$ \frac{\Delta A}{A}=|n|\frac{\Delta x}{x} $$

• for $A=c*e^{(x\pm\Delta x)}$ {c=constant}:

$$ \frac{\Delta A}{A}=\Delta x $$

• for $A=(x\pm\Delta x)+\text{or}-(y\pm\Delta y)...$ :

$$ \left(\sigma_A\right)^2 = \left(\sigma_x\right)^2 + \left(\sigma_y\right)^2

• \left(\sigma_z\right)^2 ... $$

• for $A=(x\pm\Delta x)*\text{or}/(y\pm\Delta y)...$ :

$$ \left(\frac{\sigma_A}{A}\right)^2 = \left(\frac{\sigma_x}{x}\right)^2 + n^2 \left(\frac{\sigma_y}{y}\right)^2

• m^2 \left(\frac{\sigma_z}{z}\right)^2 ... $$