第$8$天池塘长满,第$7$天水草占池塘的$\frac {1}{2},$
$ $第$6$天水草占池塘的$\frac {1}{2}×\frac {1}{2}=\frac {1}{4},$
$ $第$5$天水草占池塘的$\frac {1}{4}×\frac {1}{2}=\frac {1}{8},$
$ $第$4$天水草占池塘的$\frac {1}{8}×\frac {1}{2}=\frac {1}{16}。$
答:第$4$天结束时水草长满了池塘的$\frac {1}{16}。$
