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How heavy is 623.68950875 grams?

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It's about as heavy as a Basketball.
(NBA official ball standards, Size 7)
A regulation NBA basketball, manufactured by Spalding, is known as a Size 7 ball and weighs 623.68950875 g. These balls have 4,118 pebbles each with a diameter of 2.5 mm
It's about one-and-a-half times as heavy as a Football (Soccer).
In other words, the weight of a Football (Soccer) is 0.67 times 623.68950875 grams.
(a.k.a. Soccer, a.k.a. Association Football) (FIFA Law 2 specification)
According to FIFA's Law of the Game number 2, a football must weigh between 410 g and 450 g. An artifact on display at the Smith Art Gallery in Museum in Stirling, Scotland is said to be the world's oldest football and is about one-third to one-half the size of a modern football.
It's about one-and-a-half times as heavy as a Football (American).
In other words, 623.68950875 grams is 1.51724137931 times the weight of a Football (American), and the weight of a Football (American) is 0.6590909090911 times that amount.
(a.k.a. "pigskin") (NFL standard)
Per National Football League official rules, an American football must weigh between 396.89332375 g and 425.242846875 g. Because of NFL regulations, ceremonial considerations, and backup requirements, each NFL Superbowl requires the manufacture of 144 balls exclusively for the event.
It's about three-fifths as heavy as a liter of Water.
In other words, 623.68950875 grams is 0.623672 times the weight of a liter of Water, and the weight of a liter of Water is 1.603407 times that amount.
(fresh; 4° C / 39.2° F; maximum density)
Contrary to popular belief, 1 liter (0.0.264172052358148 gal) of water at 4° C / 39.2° F (its point of maximum density) weighs 1,000.028 grams rather than 1 kg exactly. The total volume of water on the planet Earth is about 13,590,000,000,000,000,000 (13.59 quntillion) L (3,590,000,000,000,000,000 gallons).
It's about one-and-four-fifths times as heavy as a Can of Soup.
In other words, the weight of a Can of Soup is 0.56 times 623.68950875 grams.
(for Campbell''s Condensed Tomato Soup, 317.9 ml)
A can of Campbell''s Tomato Soup weighs 350 g. Cans have been used to store soup and other foods since their invention in 1913, but a dedicated can opener was not developed until cans began to use thinner materials — prior to that time, cans were usually opened using various blunt instruments and tools.
It's about two times as heavy as a Human Heart.
In other words, the weight of a Human Heart is 0.5 times 623.68950875 grams.
(human; adult)
The average human heart weighs about 310 g. Each minute, the heart pumps between 10 and 20 liters (3 to 5 gallons) of blood through its chambers.
It's about half as heavy as a Human Brain.
In other words, 623.68950875 grams is 0.462 times the weight of a Human Brain, and the weight of a Human Brain is 2.16 times that amount.
(adult)
The average weight of an adult human brain is between 1,300 and 1,400 g. In humans and primates, sight and vision utilize about 30 different parts of the brain which together account for about half of the brain's size.