We analyse abstract data types that model numerical structures with a concept of error. Specifically, we focus on arithmetic data types that contain an error value
\(\bot\)
whose main purpose is to always return a value for division. To rings and fields, we add a division operator
\(x/y\)
and study a class of algebras called
common meadows
wherein
\(x/0=\bot\)
. The set of equations true in all common meadows is named the
equational theory of common meadows
. We give a finite equational axiomatisation of the equational theory of common meadows and prove that it is complete and that the equational theory is decidable.