Unless you have a specific reason for closing them then just leave them. It uses more battery power to load and unload things from memory plus the screen time of you actually doing the task. If iOS needs more memory it will close an app by itself. Well not actually close, suspend it.
The bolded part is only true to a certain point. Especially on 1gb ram devices. It doesn't take much to have an app kicked from ram. Say you open app 1, then over the course of 20-25 minutes or so, you've opened 2-3 more apps. Odds are very likely app 1 has been kicked out of ram by those 2-3 other apps you used. App 1 would need to fully relaunch again, thus losing out on that precious "battery saving".
In the case of the new phones with 2gb of ram. It can still happen but takes much longer to do it. Since 2-3 apps wouldn't tie up all the ram and kick out app 1 as quickly.