You and your fellow legionaries have just conquered a neighboring village, and the Prelate has ordered per tradition that the survivors be decimated and the victims' heads delivered to him in a sack as proof of the deed.
Sadly, he's a little new on the job (and more than a little bloodthirsty), and incorrectly believes that "decimate" means to reduce the population to 1/10th its original size. Your Captain, on the other hand, is a seasoned veteran and he knows that it really only means to reduce the population by 1/10th.
Unfortunately, these two officers have very limited means of communication. The Prelate can only communicate with the Captain by sending an order to decimate the survivors, and the Captain can only communicate with the Prelate by sending him a sack full of heads.
Since the Prelate knows exactly how many villagers there were to start with, and will not be satisfied until his definition of "decimation" has occurred, how many times will he have to give the order before his expectations are met?
(Note: I'm looking for a mathematical answer. You could just do this on a calculator but that's not how this is intended to be solved. You may assume all rounding is to the nearest integer, though it shouldn't make much of a difference.)