The compound "thirty-odd" is a relatively modern English construction, combining the cardinal number "thirty" with the adjective "odd". The term "odd" in this context derives from its 16th-century sense of "left over, remaining", used after a round number to indicate a surplus. This usage originates from the earlier notion of an "odd" number being one left over when pairs are made, or one exceeding an even count. Thus, "thirty-odd" literally means "thirty plus an indefinite extra amount", a logical extension from numerical irregularity to signify an approximate quantity slightly above the specified number.

Structure: thirty (number) + odd (indefinite) - thirty: From Old English þrītiġ, meaning "three tens". A Germanic compound number. - odd: From Old Norse oddi, meaning "point of land, triangle", later "third or unmatched number", evolving to mean "strange, irregular, or indefinite".