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.
[196.606, -86.123, 169.21, 28.574, -13.886, 149.466, 48.27, 184.201, 203.036, 132.427]