Turn off the hot-water heater in your RV.
Mix one teaspoon of chlorine (or according to packaging directions) per 100 gallons of water into a gallon jug.
Dilute by filling the gallon the rest of the way with water.
Pour your mixture into the tank while you simultaneously fill it with water. Fill it completely.
Turn on all the faucets inside the RV. Remember to flush the toilet and turn on the shower.
Turn off the water when you can smell chlorine. This means you have flushed out the old water. You can safely leave this mixture in the tank without flushing it out. It will not harm components like straight bleach, and it is safe to drink.