Coasting out of gear saves fuel
Nowadays this statement is false. It used to be quite a common practice to try to save fuel by taking your car out of gear when driving down hills and slopes but the fuel system in modern cars means that coasting is no longer beneficial to energy efficiency.
Is it better to idle in neutral or park? Even when parked while waiting at signals an engine will continue to consume fuel while idling. In general, for an automatic transmission, at a stop while idling produces a load on the engine and worsens fuel efficiency. Neutral idle alleviates this fuel consumption and helps improve mileage.