AA batteries (the bigger ones) have more capacity than AAA batteries but for some applications like e.g alarm clocks, it does not make much of a difference. The AA batteries are a little fatter and 6mm higher. With a bit of cardboard you can build an adapter. I used a short screw for the contact. The below photos show how it works. The AAA battery simply slides into this adapter and then you can use it anywhere where you would normally use AA batteries.
Components used to build the adapter: brown cardboard from a toilet paper roll (wrapped 3 times around the AAA battery), thicker white cardboard, short machine screw
AA battery next to a AAA battery in the adapter; I have glued the white cardboard with normal school glue on top of the brown cardboard
