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.
[196.113, 189.98, 46.856, -49.77, 67.858, 42.376, 117.534, 173.844, 43.76, -80.7]