hundredth (adj., n.)

"1 more than ninety-nine, ten times ten; the number which is one more than ninety-nine; a symbol representing this number;" Old English hundred "the number of 100, a counting of 100," from Proto-Germanic *hunda-ratha- (source also of Old Frisian hundred, Old Saxon hunderod, Old Norse hundrað, German hundert); first element is Proto-Germanic *hundam "hundred" (cognate with Gothic hund, Old High German hunt), from PIE *km-tom "hundred," reduced from *dkm-tom- (source also of Sanskrit satam, Avestan satem, Greek hekaton, Latin centum, Lithuanian šimtas, Old Church Slavonic suto, Old Irish cet, Breton kant "hundred"), suffixed form of root *dekm- "ten."

The second element is Proto-Germanic *rath "reckoning, number" (as in Gothic raþjo "a reckoning, account, number," garaþjan "to count;" from PIE root *re- "to reason, count"). The common word for the number in Old English was simple hund, and Old English also used hund-teontig.

In Old Norse hundrath meant 120, that is the long hundred of six score, and at a later date, when both the six-score hundred and the five-score hundred were in use, the old or long hundred was styled hundrath tolf-roett ... meaning "duodecimal hundred," and the new or short hundred was called hundrath ti-rætt, meaning "decimal hundred." "The Long Hundred and its use in England" was discussed by Mr W.H. Stevenson, in 1889, in the Archæological Review (iv. 313-27), where he stated that amongst the Teutons, who longest preserved their native customs unimpaired by the influence of Latin Christianity, the hundred was generally the six-score hundred. The short hundred was introduced among the Northmen in the train of Christianity. [Transactions of the Lancashire and Cheshire Antiquarian Society, 1907]

Meaning "division of a county or shire with its own court" (still in some British place names and U.S. state of Delaware) was in Old English and probably represents 100 hides of land. The Hundred Years War (which ran intermittently from 1337 to 1453) was first so called in 1874. The original Hundred Days was the period between Napoleon's restoration and his final abdication in 1815.

word-forming element making ordinal numbers (fourth, tenth, etc.), Old English -ða, from Proto-Germanic *-tha- (cognates: Gothic -da, -ta, Old High German -do, -to, Old Norse -di, -ti), from PIE *-to-, also *-eto-, *-oto-, suffix forming adjectives "marking the accomplishment of the notion of the base" [Watkins].

Cognate with Sanskrit thah, Greek -tos, Latin -tus; Sanskrit ta-, Lithuanian and Old Church Slavonic to, Greek to "the," Latin talis "such;" Greek tēlikos "so old, of such an age," Old Church Slavonic toli "so, to such a degree," toliku "so much," Russian toliko "only;" also see -ed.