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.
[34.351, -16.627, -97.579, 87.924, -49.177, 246.18, -47.001, 49.77, -51.755, 59.436]