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How heavy is 623.689508750 grams?

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It's about six-and-a-half times as heavy as a Deck of Cards.
In other words, the weight of a Deck of Cards is 0.150 times 623.689508750 grams.
(ISO 216 B8 size, a.k.a. "poker size" 63 x 88 mm, 52-card deck)
A deck of 52 ISO 216 B8-size playing cards weighs 94 g. Utilizing nearly 3,700 decks, the record-holding largest card tower was built in early 2010, stood over 3.5 m (11 ft), and weighed over 230,000 grams.
It's about nine-and-a-half times as heavy as a Battery (C).
In other words, the weight of a Battery (C) is 0.10 times 623.689508750 grams.
(Alkaline)
A "C" size battery weighs 65 g. C batteries are typically used in medium-drain devices such as musical instruments.
It's about one-tenth as heavy as a Gallon of Paint.
In other words, the weight of a Gallon of Paint is 10 times 623.689508750 grams.
(excluding container; average weight)
A gallon of paint weighs about 5,000 grams. Every day, 10,000,000 L (3,000,000 gal) of paint are applied in the United States.
It's about one-tenth as heavy as a Cat.
In other words, the weight of a Cat is 10 times 623.689508750 grams.
(Felis catus) (Domestic; healthy weight)
The average domestic cat should weigh between 5,000 grams. Cats are known for their righting reflex, which allows them to land on their feet and survive falls from heights of 1 m (3 ft) up to about 21 m.
It's about eleven times as heavy as a Tennis Ball.
In other words, 623.689508750 grams is 10.80 times the weight of a Tennis Ball, and the weight of a Tennis Ball is 0.0926 times that amount.
(ITF Standard; for Type 2 ball)
Per International Tennis Federation standard, regulation tennis balls must weigh about 56.0 g to 59.4 g. Competition balls are also tested for bounce height, with the standards requiring that a ball dropped from 254 cm must bounce back to a height of 135 cm to 147 cm.
It's about one-tenth as heavy as a Bowling Ball.
In other words, 623.689508750 grams is 0.0916666667 times the weight of a Bowling Ball, and the weight of a Bowling Ball is 10.90909090 times that amount.
(most common selection among male bowlers)
With an allowable range of 4,989.516070 grams, the most-preferred bowling ball weight among adult, male bowlers is 6,803.885550 grams. Because regulation balls measure the same diameter irrespective of their weight, ball density varies by size and balls weighing less than about 5,000 grams will float in water.
It's about thirteen-and-a-half times as heavy as a Golf Ball.
In other words, 623.689508750 grams is 13.580 times the weight of a Golf Ball, and the weight of a Golf Ball is 0.07364 times that amount.
(per R&A USGA Rules of Golf; maximum rule weight)
According to the Rules of Golf (as approved by the United States Golf Association and the Rules Committee of the Royal and Ancient Golf Club of Saint Andrews), golf balls must weigh no more than 45.93 g. Golf balls are not required to have the familiar dimpled pattern, but the design has been popular since its invention in 1905 because it reduces drag while increasing lift.