Apply the binary search algorithm in detail to search for an entry with key equal to $6\mathrm{.}8$ in an ordered map with entries consisting only of the following numerical keys:

$1\mathrm{.}6,4\mathrm{.}7,5\mathrm{.}8,6\mathrm{.}7,7\mathrm{.}5,8\mathrm{.}2,8\mathrm{.}6,9\mathrm{.}8,10\mathrm{.}4,12\mathrm{.}7,14\mathrm{.}2,14\mathrm{.}9,17\mathrm{.}8,17\mathrm{.}8,19\mathrm{.}3,23\mathrm{.}5.$