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.
[116.488, 220.111, 166.776, 8.984, -68.034, 244.425, 58.269, 79.185, -20.93, -47.64]