In this task, you will be given a list of numbers. The goal is to divide all the numbers in the list by a constant such that the sum of the resulting list is 1. The output should be rounded to 3 decimals.

[85.604, -42.553, -19.748, -88.498, 112.054, -52.975, 156.953, 108.598]
[ 0.33  -0.164 -0.076 -0.341  0.432 -0.204  0.605  0.419]