如图，\(∆ABC \)中，\(BC= α \)，若\(D_{1}\)、\(E_{1}\)分别是\(AB\)、\(AC\)的中点，则\(D_{1}E_{1}= \dfrac{1}{2} α \)；若\(D_{2、}E_{2}\)分别是\(D_{1}BE_{1}C\)的中点，则\(D_{2}E_{2}= \dfrac{1}{2}( \dfrac{α}{2}+α)= \dfrac{3}{4}α \)；若\(D_{3、}E_{3}\)分别是\(D_{2}B\)，\(E_{2}C\)的中点，则\(D_{3}E_{3}= \dfrac{1}{2}\left( \dfrac{3}{4}α+α\right)= \dfrac{7}{8}α \)；\(……\)若\(D_{8、}E_{8}\)分别是\(D_{7}\)B、\(E_{7}C\)的中点，则\({{D}_{8}}{{E}_{8}}=\)____________。