Weapon damage :

Is rounded : Yes
BDM = Base damage modifier
RB    = Robot bonuses
WC   = Weapon control bonus from extensions (Basic magneto, etc..)
TA    = Target Analysis extension : 1% bonus per level
DT    = Damage tuning bonus : Bonus depends on module
q      = Quantity of tunings
             
RB   = Extension bonus x extension level
WC  = Extension bonus x extension level
TA   = Extension bonus x extension level
DT   = Module bonus

             
DMG = BDM * (1+(RB+WC)) * (1+TA) * (1+DT)^q

Example :
Ship :
- Yagel (5% bonus per Basic robotics extension level)
Extensions :
- Basic robotics level 5
- Basic Magnetostatics level 5 (3% bonus per level)
- Target Analysis level 4
Modules :
- Nuimtec Rowo Light Em Gun (135% base damage)
- Standard Magnetic Weapon Tuning X 3 (5% bonus)

135*(1+(5*0.05 + 5*0.03) * (1+(4*0.01)) * (1+0.05)^3
135*1.4*1.04*1.157625 = 227.54277
Result is rounded to 228

Turret Falloff :

Is rounded : Yes
BFO = Base falloff
RB  = Robot bonuses
IFO = Improved Falloff extension

RB = Extension bonus x extension level
IFO = Extension bonus x extension level

FO = BFO *  1+(RB+IFO)

Example :
Ship :
- Yagel (5% bonus per Basic robotics extension level)
Extensions :
- Basic robotics level 5
- Improved falloff level 4 (3% bonus per level)
Modules :
- Nuimtec Rowo Light Em Gun (50m base falloff)

50*(1+(5*0.05 + 4*0.03)) = 68.5
Result is rounded to 69m