Does switching from drive to neutral save gas?

ive gotten into the habit of doing such while im driving down a hill or a long stretch of road and i feel like i have enough momentum to cruise. if i start to slow down too much, i switch back to drive. is this ok or can it damage my engine? and if it is ok, can it also save gas? i drive an automatic 2004 chevrolet... show more ive gotten into the habit of doing such while im driving down a hill or a long stretch of road and i feel like i have enough momentum to cruise. if i start to slow down too much, i switch back to drive. is this ok or can it damage my engine? and if it is ok, can it also save gas? i drive an automatic 2004 chevrolet aveo if that helps?
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