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How heavy is 6.70 tons?

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It's about 150,000 times as heavy as a Golf Ball.
In other words, 6.70 tons is 132,300 times the weight of a Golf Ball, and the weight of a Golf Ball is 0.0000075590 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 0.000050630 tons. 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 one-one-hundred-fifty-thousandth as heavy as The Golden Gate Bridge.
In other words, 6.70 tons is 0.000007550 times the weight of The Golden Gate Bridge, and the weight of The Golden Gate Bridge is 132,000 times that amount.
(San Francisco, California and Marin County, California) (Post 1986 weight reduction; total weight of bridge, anchorage, and approaches)
Following the completion of the 1986 project to eliminate excess material, the total weight of the Golden Gate Bridge — including its anchorages and approaches — is 887,000 tons. The two main cables in the spanning the bridge are spun out of a total of 129,000 km (80,200 mi) of wire.
It's about 200,000 times as heavy as a Light Bulb.
In other words, 6.70 tons is 180,000 times the weight of a Light Bulb, and the weight of a Light Bulb is 0.00000560 times that amount.
(a.k.a. lamp) (for A19-size, 60w, incandescent bulb by Bulbrite; package weight)
A standard, sixty-watt light bulb weighs about 0.0000380 tons. The tightly-coiled filament inside a bulb of this size would measure about 579mm if uncoiled and stretched out.
It's about 250,000 times as heavy as a Battery (AA).
In other words, the weight of a Battery (AA) is 0.00000400 times 6.70 tons.
(Alkaline)
An "AA" size battery weighs 0.0000260 tons. 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 times as heavy as a Mouse.
In other words, 6.70 tons is 290,000 times the weight of a Mouse, and the weight of a Mouse is 0.00000340 times that amount.
(a.k.a. "House mouse", Mus musculus) (adult)
The weight of a mouse is typically an average of 0.0000230 tons. 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 times as heavy as a Compact disc.
In other words, 6.70 tons is 410,000 times the weight of a Compact disc, and the weight of a Compact disc is 0.00000240 times that amount.
(a.k.a. CD)
A compact disc typically weighs 0.0000170 tons. 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 500,000 times as heavy as a Battery (AAA).
In other words, the weight of a Battery (AAA) is 0.00000200 times 6.70 tons.
(Alkaline)
An "AAA" size battery weighs 0.0000130 tons. 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.