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How heavy is 415 carats?

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It's about nine-tenths as heavy as a Deck of Cards.
In other words, 415 carats is 0.910 times the weight of a Deck of Cards, and the weight of a Deck of Cards is 1.10 times that amount.
(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 460 carats. 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 1,100,000 carats.
It's about one-and-three-tenths times as heavy as a Battery (C).
In other words, the weight of a Battery (C) is 0.770 times 415 carats.
(Alkaline)
A "C" size battery weighs 320 carats. C batteries are typically used in medium-drain devices such as musical instruments.
It's about one-and-a-half times as heavy as a Tennis Ball.
In other words, 415 carats is 1.480 times the weight of a Tennis Ball, and the weight of a Tennis Ball is 0.6760 times that amount.
(ITF Standard; for Type 2 ball)
Per International Tennis Federation standard, regulation tennis balls must weigh about 281 carats. 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 three-fifths as heavy as a Battery (D).
In other words, 415 carats is 0.6310 times the weight of a Battery (D), and the weight of a Battery (D) is 1.580 times that amount.
(Alkaline)
A "D" size battery weighs 658 carats. The D size battery is the oldest of the modern battery sizes, first invented by the National Carbon Company in 1898.
It's about three-fifths as heavy as a Baseball.
In other words, 415 carats is 0.586109175376520 times the weight of a Baseball, and the weight of a Baseball is 1.70616677235530 times that amount.
(MLB rules)
Per Major League Baseball rules, a baseball must weigh between 690.789473685330 carats and 725.32894736960 carats. A major league pitcher can throw a baseball at up to 150 kph (91 mph) (with a fastball pitch), with record-setting pitches as fast as 171 kph (106 mph).
It's about one-and-nine-tenths times as heavy as a Golf Ball.
In other words, 415 carats is 1.8540 times the weight of a Golf Ball, and the weight of a Golf Ball is 0.53940 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 223.80 carats. 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.
It's about half as heavy as a Billiard Ball.
In other words, 415 carats is 0.522401656313850 times the weight of a Billiard Ball, and the weight of a Billiard Ball is 1.91423589093530 times that amount.
(American-style, WPA specifications)
Per the World Pool-Billiard Association, a billiard ball weight must weigh between 759.868421053870 carats and 828.94736842240 carats. According to legend, the difficulty in obtaining elephant ivory for the manufacture of billiard balls in the 19th century inspired the search for a replacement material, which led to the development of the first industrial plastic.