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How heavy is 0.0000120 tonnes?

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It's about as heavy as a Battery (AAA).
(Alkaline)
An "AAA" size battery weighs 0.0000120 tonnes. 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 four-fifths as heavy as a Compact disc.
In other words, the weight of a Compact disc is 1.30 times 0.0000120 tonnes.
(a.k.a. CD)
A compact disc typically weighs 0.0000150 tonnes. 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 one-and-seven-tenths times as heavy as an Eye (Human).
In other words, the weight of an Eye (Human) is 0.590 times 0.0000120 tonnes.
(adult)
A fully developed eye (in a person over the age of thirteen), weighs about 0.00000710 tonnes. 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 three-fifths as heavy as a Mouse.
In other words, 0.0000120 tonnes is 0.570 times the weight of a Mouse, and the weight of a Mouse is 1.80 times that amount.
(a.k.a. "House mouse", Mus musculus) (adult)
The weight of a mouse is typically an average of 0.0000210 tonnes. 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 half as heavy as a Battery (AA).
In other words, the weight of a Battery (AA) is 2 times 0.0000120 tonnes.
(Alkaline)
An "AA" size battery weighs 0.0000240 tonnes. AA batteries came into common use during World War II and were given their name by the American National Standards Institute (ANSI) Committee C18 because they were smaller than the "A" size batteries which were invented first.
It's about two times as heavy as a sheet of Paper.
In other words, the weight of a sheet of Paper is 0.50 times 0.0000120 tonnes.
(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 0.009 tonnes, 8.5 inch x 11 inch paper is 0.002 tonnes, each sheet weighing 0.00000500 tonnes. Paper of this size has a thickness of 0.004 caliper (0.1 mm).
It's about two times as heavy as a Quarter.
In other words, 0.0000120 tonnes is 2.1160 times the weight of a Quarter, and the weight of a Quarter is 0.47260 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 0.000005670 tonnes each. In answer to the common riddle, there are 119 ridges around the edge of the coin in its current design.