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How heavy is 6.70 tons?

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It's about 850,000 times as heavy as an Eye (Human).
In other words, the weight of an Eye (Human) is 0.00000120 times 6.70 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 times as heavy as a sheet of Paper.
In other words, the weight of a sheet of Paper is 0.000001000 times 6.70 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 one-one-millionth as heavy as The Great Pyramid of Giza.
In other words, 6.70 tons is 0.000001000 times the weight of The Great Pyramid of Giza, and the weight of The Great Pyramid of Giza is 1,000,000 times that amount.
(a.k.a. Pyramid of Khufu, a.k.a. Pyramid of Cheops) (Cairo, Egypt)
The Great Pyramid of Giza has an estimated mass of 6,500,000 tons. The 2,300,000 stones used in the construction of the pyramid weighed an average 2.50 tons and were quarried from distances of up to 805 km (500 mi) away.
It's about 1,000,000 times as heavy as a Quarter.
In other words, 6.70 tons is 1,072,000 times the weight of a Quarter, and the weight of a Quarter is 0.00000093280 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 times as heavy as a Die (Dice).
In other words, the weight of a Die (Dice) is 0.000000670 times 6.70 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 times as heavy as a Penny.
In other words, the weight of a Penny is 0.000000420 times 6.70 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 times as heavy as a Playing Card.
In other words, the weight of a Playing Card is 0.000000290 times 6.70 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.