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.
[162.868, 109.38, -79.491, 191.325, 43.996, 163.118, 14.367, 219.224, -51.994, -81.541]