You're LP tank is completely empty... you know the capacity listed on it says 15gal... but they only filled it to 12gal. What gives?

Long story short, it's for your safety. In order to allow room for the gas to expand with temperature differences, a LP tank should only ever be filled to a maximum 80% of its capacity. Failure to do so could cause damage or injury.
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Your LP tank is fitted with an OPD (Overflow Prevention Device) to help minimize the risk, but the best way to be sure is to have your LP tank filled at a certified filling station.