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How heavy is 0.0001 tons?

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It's about as heavy as a Deck of Cards.
In other words, the weight of a Deck of Cards is 1 times 0.0001 tons.
(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 0.0001 tons. 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 0.250 tons.
It's about one-and-two-fifths times as heavy as a Battery (C).
In other words, the weight of a Battery (C) is 0.710 times 0.0001 tons.
(Alkaline)
A "C" size battery weighs 0.0000720 tons. C batteries are typically used in medium-drain devices such as musical instruments.
It's about two-thirds as heavy as a Battery (D).
In other words, 0.0001 tons is 0.6720 times the weight of a Battery (D), and the weight of a Battery (D) is 1.490 times that amount.
(Alkaline)
A "D" size battery weighs 0.000149 tons. The D size battery is the oldest of the modern battery sizes, first invented by the National Carbon Company in 1898.
It's about one-and-three-fifths times as heavy as a Tennis Ball.
In other words, 0.0001 tons is 1.570 times the weight of a Tennis Ball, and the weight of a Tennis Ball is 0.6370 times that amount.
(ITF Standard; for Type 2 ball)
Per International Tennis Federation standard, regulation tennis balls must weigh about 0.00006360 tons. 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 Baseball.
In other words, 0.0001 tons is 0.624390243902440 times the weight of a Baseball, and the weight of a Baseball is 1.60156250 times that amount.
(MLB rules)
Per Major League Baseball rules, a baseball must weigh between 0.00015625 tons and 0.0001640625 tons. 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 three-fifths as heavy as a Billiard Ball.
In other words, 0.0001 tons is 0.556521739130430 times the weight of a Billiard Ball, and the weight of a Billiard Ball is 1.7968750 times that amount.
(American-style, WPA specifications)
Per the World Pool-Billiard Association, a billiard ball weight must weigh between 0.000171875 tons and 0.0001875 tons. 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.
It's about three-fifths as heavy as a Puck (Hockey).
In other words, 0.0001 tons is 0.556521739130430 times the weight of a Puck (Hockey), and the weight of a Puck (Hockey) is 1.7968750 times that amount.
(Ice hockey)
A standard ice hockey puck weighs between 0.000171875 tons and 0.0001875 tons. Hockey pucks can be shot or passed at speeds of up to 160 kph (99 mph) during games.