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How heavy is 1 grams?

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It's about one-fifth as heavy as a sheet of Paper
In other words, the weight of a sheet of Paper is 5 times 1 grams.
(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 9,100 grams, 8.5 inch x 11 inch paper is 2,000 grams, each sheet weighing 5 g. Paper of this size has a thickness of 0.004 caliper (0.1 mm).
It's about one-fifth as heavy as a Quarter
In other words, 1 grams is 0.17640 times the weight of a Quarter, and the weight of a Quarter is 5.6690 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 5.670 g each. In answer to the common riddle, there are 119 ridges around the edge of the coin in its current design.
It's about one-tenth as heavy as an Eye (Human)
In other words, 1 grams is 0.140 times the weight of an Eye (Human), and the weight of an Eye (Human) is 7.10 times that amount.
(adult)
A fully developed eye (in a person over the age of thirteen), weighs about 7.10 grams. 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 one-tenth as heavy as a Battery (AAA)
In other words, the weight of a Battery (AAA) is 12 times 1 grams.
(Alkaline)
An "AAA" size battery weighs 12 g. 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 one-fifteenth as heavy as a Compact disc
In other words, the weight of a Compact disc is 15 times 1 grams.
(a.k.a. CD)
A compact disc typically weighs 15 g. 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-twentieth as heavy as a Mouse
In other words, the weight of a Mouse is 21 times 1 grams.
(a.k.a. "House mouse", Mus musculus) (adult)
The weight of a mouse is typically an average of 12 to 30 g. 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 one-twenty-fifth as heavy as a Battery (AA)
In other words, the weight of a Battery (AA) is 24 times 1 grams.
(Alkaline)
An "AA" size battery weighs 24 g. 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.