We attached a round-bottomed flask to a vacuum pump and sucked the air out. We sealed the empty flask with a Hoffman clip and put it into a tub on the chemical balance. We zeroed the scales. Then we opened the Hoffman clip. We could hear a loud hiss as the air rushed in to fill the vacuum.
400 cubic centimetres of air had rushed in and had a mass of 0.5 grams. That makes the density of air to be 0.00125 grams per cubic centimetre or 1.25 kg per cubic metre.