A careful distinction needs to be made between abstract quantities and measurable quantities. The multiplication and division rules of quantity calculus are applied to SI base units (which are measurable quantities) to define SI derived units, including dimensionless derived units, such as the radian (rad) and steradian (sr) which are useful for clarity, although they are both algebraically equal to 1. Thus there is some disagreement about whether it is meaningful to multiply or divide units. Emerson suggests that if the units of a quantity are algebraically simplified, they then are no longer units of that quantity. Johansson proposes that there are logical flaws in the application of quantity calculus, and that the so-called dimensionless quantities should be understood as "unitless quantities".