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How heavy is 6,500 tons?

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It's about 500,000,000 times as heavy as a Battery (AAA).
In other words, the weight of a Battery (AAA) is 0.00000000200 times 6,500 tons.
(Alkaline)
An "AAA" size battery weighs 0.0000130 tons. Batteries are named by the American National Standards Institute (ANSI) Committee C18 and AAA batteries were given their name because they were smaller than the "AA" and "A" size batteries which were invented first.
It's about 850,000,000 times as heavy as an Eye (Human).
In other words, the weight of an Eye (Human) is 0.00000000120 times 6,500 tons.
(adult)
A fully developed eye (in a person over the age of thirteen), weighs about 0.00000780 tons. The pupil of the eye varies depending on the amount of light it is exposed to, but typically measures about 4 mm across.
It's about 1,000,000,000 times as heavy as a sheet of Paper.
In other words, the weight of a sheet of Paper is 0.000000001000 times 6,500 tons.
(for US Letter, a.k.a. ANSI A; 215.9mm by 279.4mm (8.5 in x 11 in); 20lb)
The weight of a ream (500 sheets) of 0.01 tons, 8.5 inch x 11 inch paper is 0.002 tons, each sheet weighing 0.00000600 tons. Paper of this size has a thickness of 0.004 caliper (0.1 mm).
It's about 1,000,000,000 times as heavy as a Quarter.
In other words, 6,500 tons is 1,040,000,000 times the weight of a Quarter, and the weight of a Quarter is 0.00000000096150 times that amount.
(United States quarter-dollar coin) (a.k.a. Quarter dollar, a.k.a. America the Beautiful quarter, a.k.a. two bits)
The America the Beautiful series quarters, which began to enter circulation in 2017, weigh 0.000006250 tons each. In answer to the common riddle, there are 119 ridges around the edge of the coin in its current design.
It's about 1,500,000,000 times as heavy as a Die (Dice).
In other words, the weight of a Die (Dice) is 0.000000000710 times 6,500 tons.
(for six-sided, 16 mm, rounded cube)
A die, of the size most commonly used in board games and casinos, typically weight 0.00000450 tons. The use of dice and dice-like tools predates written history, with the oldest known examples belonging to a 5,000-year old backgammon set uncovered during an archaeological dig in modern-day Iran.
It's about 2,500,000,000 times as heavy as a Penny.
In other words, the weight of a Penny is 0.000000000420 times 6,500 tons.
(United States) (formally one-cent coin) (Union shield design, 2010-present)
The weight of a United States penny is 0.00000280 tons. According to a 2010 report by the United States Mint, the cost of manufacturing and distributing a penny is $0.0179 — more than its face-value.
It's about 3,500,000,000 times as heavy as a Playing Card.
In other words, the weight of a Playing Card is 0.000000000300 times 6,500 tons.
(ISO 216 B8 size, 2.5" x 3.5")
A single ISO 216 B8-size playing card weighs 0.00000200 tons. Although this size is the most common home playing card, many casinos use "bridge size" cards — 2,640 sq. mm (4.036 sq. in) smaller in area.