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.
[88.646, 159.172, 137.102, -65.719, -1.901, 189.28, 230.225, 12.846, 222.446, 81.686]