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3/0 AWG is a guage ( 3 aught)
3 AWG wire is way smaller than 3/0
In area a 3 guage wire has 52,620 circular mils
A 3/0 guage has 167,800 circular mils
and just for comparison
the 12 guage wire in your house is 6,530 circular mils
A #3 wire is about the size of a pencil, insulation included.
A 3/0 is about the size of your thumb.
This is just a small sample of AWG numbers.
On our trucks the battery cables are 2/0 AWG for ground wires off both batteries.
The positive cable between batteries is 2/0 AWG.
The positive cable from the passenger side battery to the starter is 3/0 AWG.
Gas powered vehicles use a much smaller cable.
This is why most jumper cables do not do the trick when you try to jump your truck. They were meant to jump gasoline vehicles.
I carry a set that is made out of welding lead. They do work.