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How heavy is 370 grains?

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It's about one-and-one-tenth times as heavy as a Mouse
In other words, the weight of a Mouse is 0.910 times 370 grains.
(a.k.a. "House mouse", Mus musculus) (adult)
The weight of a mouse is typically an average of 320 grains. 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-and-three-fifths times as heavy as a Compact disc
In other words, the weight of a Compact disc is 0.630 times 370 grains.
(a.k.a. CD)
A compact disc typically weighs 230 grains. 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 two times as heavy as a Battery (AAA)
In other words, the weight of a Battery (AAA) is 0.50 times 370 grains.
(Alkaline)
An "AAA" size battery weighs 190 grains. 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 three-and-a-half times as heavy as an Eye (Human)
In other words, the weight of an Eye (Human) is 0.290 times 370 grains.
(adult)
A fully developed eye (in a person over the age of thirteen), weighs about 110 grains. 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 four times as heavy as a Quarter
In other words, 370 grains is 4.2290 times the weight of a Quarter, and the weight of a Quarter is 0.23650 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 87.50 grains each. In answer to the common riddle, there are 119 ridges around the edge of the coin in its current design.
It's about five times as heavy as a sheet of Paper
In other words, 370 grains is 4.80 times the weight of a sheet of Paper, and the weight of a sheet of Paper is 0.210 times that amount.
(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 140,000 grains, 8.5 inch x 11 inch paper is 31,000 grains, each sheet weighing 77 grains. Paper of this size has a thickness of 0.004 caliper (0.1 mm).
It's about six times as heavy as a Die (Dice)
In other words, 370 grains is 5.80 times the weight of a Die (Dice), and the weight of a Die (Dice) is 0.170 times that amount.
(for six-sided, 16 mm, rounded cube)
A die, of the size most commonly used in board games and casinos, typically weight 63 grains. 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.