Since 1 mg = 10-3 g, and 1 ng = 10-9 g, the ratio of 100 ng to 1 mg is 10-7 / 10-3 = 10-4. That means, lower concentration / higher concentration = 0.0001 resp. with a certain amount of active ingredient, the volume ratio of lower / higher concentration is 10000.

In other words, if you take 1 ml of the solution with 1 mg/ml, then you have to add 9.999 l pure fluid, resulting in 10 l solution with 100 ng/ml.