The word 'ten-thousandth' is a modern English compound formed by combining the cardinal numbers 'ten' and 'thousand', which both trace back to common Germanic roots, with the ordinal-forming suffix '-th'. The Germanic root for 'ten', tehun, and for 'thousand', þūsundī, are themselves derived from Proto-Indo-European numerals déḱm̥ and tūsontī- respectively. The suffix '-th' originates from the Proto-Germanic ordinal suffix -dô. The logical construction is purely arithmetic: the concept represents the ordinal position or fractional unit resulting from dividing a whole into ten thousand (10,000) equal parts, directly following the pattern established for other ordinal numbers like 'hundredth' or 'millionth'.

Structure: ten + thousand + th - ten: From Old English 'tēn', 'tīen', of Germanic origin; related to Dutch 'tien' and German 'zehn'. Functions as a cardinal number. - thousand: From Old English 'þūsend', of Germanic origin; related to Dutch 'duizend' and German 'tausend'. Functions as a cardinal number. - th: A suffix from Old English '-tha', '-the', used to form ordinal numbers and fractional nouns from cardinal numbers.