Old English weorþ "significant, valuable, of value; valued, appreciated, highly thought-of, deserving, meriting; honorable, noble, of high rank; suitable for, proper, fit, capable," from Proto-Germanic *wertha- "toward, opposite," hence "equivalent, worth" (source also of Old Frisian werth, Old Norse verðr, Dutch waard, Old High German werd, German wert, Gothic wairþs "worth, worthy"), which is of uncertain origin. Perhaps a derivative of PIE *wert- "to turn, wind," from root *wer- (2) "to turn, bend." Old Church Slavonic vredu, Lithuanian vertas "worth" are considered to be Germanic loan-words. From c. 1200 as "equivalent to, of the value of, valued at; having importance equal to; equal in power to."
Old English hwile, accusative of hwil "a space of time," from Proto-Germanic *hwilo (source also of Old Saxon hwil, Old Frisian hwile, Old High German hwila, German Weile, Gothic hveila "space of time, while"), originally "rest" (compare Old Norse hvila "bed," hvild "rest"), from PIE *kwi-lo-, suffixed form of root *kweie- "to rest, be quiet." Notion of "period of rest" became in Germanic "period of time."
Now largely superseded by time except in formulaic constructions (such as all the while). Middle English sense of "short space of time spent in doing something" now only preserved in worthwhile and phrases such as worth (one's) while. As a conjunction, "during or in the time that; as long as" (late Old English), it represents Old English þa hwile þe, literally "the while that." Form whiles is recorded from early 13c.; whilst is from late 14c., with unetymological -st as in amongst, amidst. Service while-you-wait is attested from 1911.
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Definitions of worthwhile
sufficiently valuable to justify the investment of time or interest;