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.
[114.209, 12.049, 188.889, 225.001, 106.569, -99.002, -95.069, 44.671, 234.599, 140.719]