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.
[110.96, 164.374, 88.174, 138.135, 68.02, -32.426, 167.275, 69.885, -31.984, 214.158]