Archimedes principle and melting sea ice

We can use Archimedes principle to understand why there's no change in water level when ice that is floating in the water melts.

We'll imagine adding 20 grams of ice to a glass of water.  Archimedes law states that an object immersed in a fluid will experience an upward buoyant force equal to the weight of the fluid displaced.  It's this upward force that causes the ice to float.

Ice has a density of  about 0.9 g/cm3, a little bit less than the density of water (1 g/cm3).  The 20 grams of ice has a volume of about 22.2 cm3.  Once the ice is added to the water it will displace 20 cm3 of water (most of the ice is under water 20 cm3or the 22.2 cm3, only a little bit sticks out above the water).  This displaced water weighs 20 grams and provides just the upward force needed to support 20 grams of ice.  Adding the ice also brought the water level right up to the edge of the glass.

Once all the ice melts it will still have a mass of 20 grams.  But it's volume will now be 20 cm3 instead of 22.2 cm3.  So the 20 cm3 of ice water will take the space that was occupied by the 20 cm3 of submerged ice.  The displaced water is now supporting 20 grams of ice water instead of 20 grams of ice.  The ice cubes have all melted and the water level is the same as it was at the start of the demonstration.

This is a fairly long winded explanation.  See if you can boil it down to just a sentence or two.