A different approach to modeling units
While units are a built-in functionality in some OLAP databases, we need to take care of them in SSAS on our own. Usually I model units as a dimension so that the facts are linked to the unit they belong to. However, units usually must not be aggregated (like adding up meters with liters), and therefore we would set the IsAggregatable property to false. The user first has to choose a unit before the result is displayed. In some cases this may not be that clear. For (local) currency for example the values are aggregatable as long as the currency is consistent which may or may not depend of the currency unit. As long as the selection (no matter of how the filtering was done) leads to a single currency it would be possible to display the result in local currency. Whenever there is more than one currency involved, the result cannot be shown.
Taking the usual approach with the non-aggregatable unit dimension you may find a situation like below: