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How heavy is 6.70 tons?

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It's about 300,000 times as heavy as a Mouse.
In other words, 6.70 tons is 290,000 times the weight of a Mouse, and the weight of a Mouse is 0.00000340 times that amount.
(a.k.a. "House mouse", Mus musculus) (adult)
The weight of a mouse is typically an average of 0.0000230 tons. While most mice typically live two to three years, the Methuselah Mouse Prize — an award administered by a non-profit organization which advances aging-related research — was once awarded to a team of scientists whose research resulted in a mouse living just under five years.
It's about 400,000 times as heavy as a Compact disc.
In other words, 6.70 tons is 410,000 times the weight of a Compact disc, and the weight of a Compact disc is 0.00000240 times that amount.
(a.k.a. CD)
A compact disc typically weighs 0.0000170 tons. Data is stored on CDs by encoding into the track a series of tiny pits — each between 3.5 and 850 µm (0.00014 and 0.033 in) in length.
It's about 500,000 times as heavy as a Battery (AAA).
In other words, the weight of a Battery (AAA) is 0.00000200 times 6.70 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 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 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.