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How heavy is 0.420 ounces?

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It's about as heavy as a Battery (AAA).
In other words, the weight of a Battery (AAA) is 1 times 0.420 ounces.
(Alkaline)
An "AAA" size battery weighs 0.420 ounces. 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, 0.420 ounces is 0.790 times the weight of a Compact disc, and the weight of a Compact disc is 1.30 times that amount.
(a.k.a. CD)
A compact disc typically weighs 0.530 ounces. 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 0.420 ounces.
(adult)
A fully developed eye (in a person over the age of thirteen), weighs about 0.25 oz. 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, 0.420 ounces 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 0.740 ounces. 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 0.420 ounces.
(Alkaline)
An "AA" size battery weighs 0.850 ounces. 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 0.420 ounces.
(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 300 ounces, 8.5 inch x 11 inch paper is 70 ounces, each sheet weighing 0.20 ounces. 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, 0.420 ounces is 2.10 times the weight of a Quarter, and the weight of a Quarter is 0.47620 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 0.20 ounces each. In answer to the common riddle, there are 119 ridges around the edge of the coin in its current design.