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.
[206.93, -55.997, 170.578, -32.228, 94.507, 134.526, -13.853, 182.585, -31.632, 84.962]