AT expresses where something is in general terms, (in contact with the AREA that is in contact with a point in space, may also be in direct contract with a point in space)
ON expresses direct contact with a SURFACE or closeness to a surface, often when something is being supported by something else
at the bottom of a drawer... in the area that is considered the bottom of the drawer (may also be "on" the bottom)
on the bottom of the drawer....in contact with or very close to the bottom surface of the drawer
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at the bottom of the sea....in the area in contact with the bottom, may also be in direct contact with the bottom of the sea)
-The octopus lives at the bottom of the sea.
on the bottom of the sea....in contact with the surface or very close to the bottom surface
-The octopus lies in wait on the sea bottom.
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at the bottom of the bathtub....
-The soap is floating at the bottom of the bathtub. (In the area that is considered the bottom, this may also be "on" the bottom)
on the bottom of the bathtub....
-The soap is floating on the bottom of the bathtub. (very close to the bottom surface)
-The soap is lying on the bottom of the bathtub. (in contact with the bottom surface)
-The wet soap is stuck on the side of the bathtub. (in contact with the side surface)
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at the bottom of the bottle.
-There is a worm at the bottom of every bottle of real Tequila.
-I don't see it!
on the bottom of the bottle
It's right there sitting on the bottom of the bottle!