The term 'dimension' in the international system of units

The term 'dimension' as used in the International System of Units (SI) is not well defined. Moreover, the term 'quantity of dimension one' (formerly called 'dimensionless quantity', a term which is unfortunately still sometimes used) as defined in the International Vocabulary of Metrology (VIM) is mathematically unsound. In order to overcome these difficulties, a new quantity dimension, called 'dimension number', will be introduced in this paper. It will be shown that such a dimension necessarily belongs to any system of dimensions, but is not a base dimension.