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.
[169.776, 238.58, -86.145, -26.179, 17.923, 14.69, 76.686, 179.243, 243.986, 1.563]