Grams are not a measure for weight so the question is like asking how many kilometres would a dollar worth of pennies weigh!
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US cents ("pennies") minted since mid-1982 weigh 2.5 gm each. There are 100 cents in a dollar so a million dollars' worth would be 100 million pennies. At 2.5 gm each their total weight would be 250 million grams. Converting to more-manageable units, there are 1000 grams in a kilo and 1000 kilos in a tonne, so there are a million grams in one tonne. Therefore 250 million grams is 250 tonnes. A large car weighs around 2 tonnes so figure the pennies would weigh about as much as a 125 cars.
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All pennies minted after 1982 weigh 2.5 grams each. (Older pennies weigh 3.11 grams) Newer cents are made of zinc because the price of copper increased so much that a copper penny was worth more than one cent. So a roll (50 pennies) would weigh (2.5g times 50 = 125 grams) (125g divided by 28.35 ounces = 4.41oz) (4.41oz divided by 16oz =.28lb) Summary. 50 pennies (1 roll, not counting paper in the roll) (add about 1.5g for the paper) = 125 grams or = 4.41 Ounces or = .28 Pounds or = Probably almost 1/3 of a pound counting the paper.
100 pennies is worth 1 dollar or 1 pound therefore 1 million pennies = 10,000 dollars or 10,000 pounds
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