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How heavy is 6.70 tons?

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It's about 35,000 times as heavy as a Puck (Hockey).
In other words, 6.70 tons is 37,286.9565217390 times the weight of a Puck (Hockey), and the weight of a Puck (Hockey) is 0.0000268190298507460 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.
It's about 40,000 times as heavy as a Baseball.
In other words, 6.70 tons is 41,834.1463414630 times the weight of a Baseball, and the weight of a Baseball is 0.0000239039179104480 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 45,000 times as heavy as a Battery (D).
In other words, the weight of a Battery (D) is 0.00002220 times 6.70 tons.
(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-fifty-five-thousandth as heavy as The Empire State Building.
In other words, the weight of The Empire State Building is 54,300 times 6.70 tons.
(New York City, New York)
The Empire State Building weighs approximately 365,000 tons. About 4% of the building's weight is its 6,000 cu. m (200,000 cu. ft) of limestone façade.
It's about 65,000 times as heavy as a Deck of Cards.
In other words, the weight of a Deck of Cards is 0.0000150 times 6.70 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 95,000 times as heavy as a Battery (C).
In other words, the weight of a Battery (C) is 0.0000110 times 6.70 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 100,000 times as heavy as a Tennis Ball.
In other words, 6.70 tons is 105,000 times the weight of a Tennis Ball, and the weight of a Tennis Ball is 0.000009520 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.