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.
[162.912, 160.833, -20.007, -56.409, -38.276, -43.596, 223.871, 190.783, 201.588, 127.716]