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According to the US Mint, the quarter dollar is 1.75mm thick.

1.75mm x 1cm/10mm = 0.175cm

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0.175cm x 1in/2.54cm = 0.0689in

1in/0.0689in = 14.5 quarters to make a stack 1 in high

Obviously you can't stack 14.5 quarters. 15 quarters makes a stack 1.03in high. 14 quarters make a stack 0.965in high.

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Q: How many quarters do you need to make a stack 1 inch high?
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