On iOS, when you switch away from an app, the OS suspends that app so that it no longer is using processing power but it stays in RAM. There are limited exceptions of specific tasks that apps can do as background activities, but the app itself is suspended and instead relies on specific hooks that iOS leaves open for limited tasks (like fetching email).
Closing an app dumps it from RAM. That means that the next time you switch to the app, it has to load it all from flash storage into RAM. That process consumes more power than just waking the app from sleep. In most cases, the net result is that regularly quitting apps uses up more battery life than just letting the OS handle them. A well behaved app should remain dormant in RAM and only briefly tap the background activity hooks Apple left available while waiting for the user to select the app again.
Facebook, however, has a history of exploiting those background processes to run more than they are supposed to. If they were a smaller company, they'd probably have long since been kicked off the App Store. You can cut off Facebook's access to the background activity hooks under the Settings app in General -> Background Activity. Similarly, cutting it off from Location Services in Privacy will also help reduce its usage. That should be enough to wrangle the Facebook app back into proper behaviour. If that doesn't work, the next step is to delete the Facebook app and just use the website.
