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.
[197.308, 105.252, -26.372, -82.169, 188.239, 41.771, 17.439, 247.922, -31.344, 212.42]