I have a set of calipers that can measure thickness of a few inches with an unce

Question

I have a set of calipers that can measure thickness of a few inches with an uncertainity of ±0.005 inches. I measure the thickness of a deck of 52 cards and get 0.590 inch. a) If i now calculate the thickness of 1 card, what is my answer (including uncertainty) b) I can improve this result by measuring several decks together. If I want to know the thickness of 1 card with an uncertainty of only 0.00002 inch, how many decks do i need to measure? I have a set of calipers that can measure thickness of a few inches with an uncertainity of ±0.005 inches. I measure the thickness of a deck of 52 cards and get 0.590 inch. a) If i now calculate the thickness of 1 card, what is my answer (including uncertainty) b) I can improve this result by measuring several decks together. If I want to know the thickness of 1 card with an uncertainty of only 0.00002 inch, how many decks do i need to measure?

Explanation / Answer

Given number of cards = 52        Thick ness of one card                  t = 1/ 52 ( T )    where   T is thick ness of   52 cards               t = ( 1 /52 ) ( 0.590 ± 0.005 )                 = 0.01139 ± 0.000096        given t = 0.59 ± 0.00002               n   = ( 0.590 ± 0.005 )   / (  0.59 ± 0.00002 )                   n = 250 decks              

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