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How heavy is 0.680 pounds?

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It's about half as heavy as a Basketball
In other words, 0.680 pounds is 0.494545454550 times the weight of a Basketball, and the weight of a Basketball is 2.0220588235 times that amount.
(NBA official ball standards, Size 7)
A regulation NBA basketball, manufactured by Spalding, is known as a Size 7 ball and weighs 1.3750 pounds. These balls have 4,118 pebbles each with a diameter of 2.5 mm
It's about two times as heavy as a Baseball
In other words, 0.680 pounds is 2.12292682926830 times the weight of a Baseball, and the weight of a Baseball is 0.471047794117650 times that amount.
(MLB rules)
Per Major League Baseball rules, a baseball must weigh between 0.31250 pounds and 0.3281250 pounds. A major league pitcher can throw a baseball at up to 150 kph (91 mph) (with a fastball pitch), with record-setting pitches as fast as 171 kph (106 mph).
It's about two-and-a-half times as heavy as a Battery (D)
In other words, 0.680 pounds is 2.280 times the weight of a Battery (D), and the weight of a Battery (D) is 0.4390 times that amount.
(Alkaline)
A "D" size battery weighs 0.2980 pounds. The D size battery is the oldest of the modern battery sizes, first invented by the National Carbon Company in 1898.
It's about three-tenths as heavy as a liter of Water
In other words, 0.680 pounds is 0.30843420 times the weight of a liter of Water, and the weight of a liter of Water is 3.2421830 times that amount.
(fresh; 4° C / 39.2° F; maximum density)
Contrary to popular belief, 1 liter (0.0.264172052358148 gal) of water at 4° C / 39.2° F (its point of maximum density) weighs 2.2046840 pounds rather than 1 kg exactly. The total volume of water on the planet Earth is about 13,590,000,000,000,000,000 (13.59 quntillion) L (3,590,000,000,000,000,000 gallons).
It's about three-and-a-half times as heavy as a Deck of Cards
In other words, the weight of a Deck of Cards is 0.30 times 0.680 pounds.
(ISO 216 B8 size, a.k.a. "poker size" 63 x 88 mm, 52-card deck)
A deck of 52 ISO 216 B8-size playing cards weighs 0.210 pounds. Utilizing nearly 3,700 decks, the record-holding largest card tower was built in early 2010, stood over 3.5 m (11 ft), and weighed over 500 pounds.
It's about one-fourth as heavy as a Human Brain
In other words, 0.680 pounds is 0.2280 times the weight of a Human Brain, and the weight of a Human Brain is 4.390 times that amount.
(adult)
The average weight of an adult human brain is between 2.980 pounds. In humans and primates, sight and vision utilize about 30 different parts of the brain which together account for about half of the brain's size.
It's about four-and-a-half times as heavy as a Battery (C)
In other words, the weight of a Battery (C) is 0.210 times 0.680 pounds.
(Alkaline)
A "C" size battery weighs 0.140 pounds. C batteries are typically used in medium-drain devices such as musical instruments.