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.
[199.935, 208.571, 137.068, -46.86, -25.906, 212.278, 206.787, 243.437, 196.888, -77.904]