'approximativeness' is a modern English formation from the adjective 'approximative' plus the nominalizing suffix '-ness', ultimately deriving from Latin 'approximare', where 'ad-' (later assimilated to 'ap-') meant 'to/toward' and 'proximus' meant 'near'.

'approximate' entered English via Old French and Medieval Latin from Latin 'approximare' ('to bring near'); French forms like 'approximatif' influenced the adjective 'approximative', and English later formed the noun 'approximativeness' by adding '-ness' to the adjective.

Originally related to the idea of 'bringing near' or 'nearness' (from Latin), the sense shifted to denote something 'near to the actual but not exact'—hence the modern meaning of 'being approximate' or 'not exact but close'.