Help with the Double Fuel Gauge Project

13.8V/VBatt * VGuage

The Vbatt and VFg are multiplied by the fraction that represents the voltage divider .
14V/4.5V = 2.8
1/( 2.8 )=0.32142
0.32142*14V=4.49988V

Let Vin=14V
Let Vout=4.5V
Let R1=10k ohms

Then:
14V*[R2/(R1+R2)]=4.5V
14V * R2/(10k +R2)=4.5V
14R2/(10k +R2) =4.5V
4.5(10k+R2)= 14
R2
45k + 4.5R2=14R2
45k=(14-4.5)R2=9.5R2
45k/9.5=R2
R2=4.7k ohms.

[Vbatt]=> >---
|
[10k ohm]
-----------> Vout=4.5v ====> (TO ARDUINO ANALOG INPUT A0)
|
[4.7k ohm]
|
[GND]

Duplicate the above voltage divider for the Fuel Gauge out put voltage. ====> (TO ARDUINO ANALOG INPUT A1)

You now have the battery voltage and the fuel guage voltage at levels that can be read by arduino
by dividing 13.8V by Vbatt
if the battery voltage is above 13.8 the fraction is < 1
if the battery voltage is >13.8V the fraction is > 1
Multiply the fuel guage readout by this fraction and it should compensate for a low or high battery.