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How heavy is 5,900,000,000 grams?

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It's about 90,000,000 times as heavy as a Battery (C).
In other words, 5,900,000,000 grams is 91,000,000 times the weight of a Battery (C), and the weight of a Battery (C) is 0.0000000110 times that amount.
(Alkaline)
A "C" size battery weighs 65 g. C batteries are typically used in medium-drain devices such as musical instruments.
It's about 100,000,000 times as heavy as a Tennis Ball.
In other words, 5,900,000,000 grams is 102,000,000 times the weight of a Tennis Ball, and the weight of a Tennis Ball is 0.00000000980 times that amount.
(ITF Standard; for Type 2 ball)
Per International Tennis Federation standard, regulation tennis balls must weigh about 56.0 g to 59.4 g. Competition balls are also tested for bounce height, with the standards requiring that a ball dropped from 254 cm must bounce back to a height of 135 cm to 147 cm.
It's about 150,000,000 times as heavy as a Golf Ball.
In other words, 5,900,000,000 grams is 128,500,000 times the weight of a Golf Ball, and the weight of a Golf Ball is 0.0000000077820 times that amount.
(per R&A USGA Rules of Golf; maximum rule weight)
According to the Rules of Golf (as approved by the United States Golf Association and the Rules Committee of the Royal and Ancient Golf Club of Saint Andrews), golf balls must weigh no more than 45.93 g. Golf balls are not required to have the familiar dimpled pattern, but the design has been popular since its invention in 1905 because it reduces drag while increasing lift.
It's about 150,000,000 times as heavy as a Light Bulb.
In other words, the weight of a Light Bulb is 0.00000000590 times 5,900,000,000 grams.
(a.k.a. lamp) (for A19-size, 60w, incandescent bulb by Bulbrite; package weight)
A standard, sixty-watt light bulb weighs about 34 grams. The tightly-coiled filament inside a bulb of this size would measure about 579mm if uncoiled and stretched out.
It's about 250,000,000 times as heavy as a Battery (AA).
In other words, the weight of a Battery (AA) is 0.00000000400 times 5,900,000,000 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.
It's about 300,000,000 times as heavy as a Mouse.
In other words, 5,900,000,000 grams is 280,000,000 times the weight of a Mouse, and the weight of a Mouse is 0.00000000360 times that amount.
(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 400,000,000 times as heavy as a Compact disc.
In other words, 5,900,000,000 grams is 390,000,000 times the weight of a Compact disc, and the weight of a Compact disc is 0.00000000260 times that amount.
(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.