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.
[111.206, 224.176, 99.659, 23.142, 227.709, -24.943, 120.616, -53.084, 93.619, -37.088]