Ihave a set of calipers that can measure thickness of a few inches with an uncertainty 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 0.2 inch, how many decks do i need to measure?

The required number of decks to measure the uncertainty is 5.

Given data:

The number of cards is, 52.

Uncertainty with thickness is, 0.590 ±0.005 inches.

(a)

Since this is thickness of all the cards, to get the thickness of a single card we divide the total thickness by the number of cards. So uncertainty in thickness for 1 card is,

Considering that thickness is given to 3 significant figures while uncertainty is to 1 significant figure, the final answer should also confirm to these hence giving the first part of the answer to 3 significant figures while second part to 1 significant figure yields 0.0113 ±0.0001 inches.

Thus, we can conclude that the required thickness uncertainty of one card is  0.0113 ±0.0001 inches.

(b)

Let the cards have uncertainty of 0.0001 inches and the number of decks, n required to create uncertainty of 0.00002 inch is given as.

Thus, we can conclude that the required number of decks to measure the uncertainty is 5.

Learn more about the uncertainties here:

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(a) 0.0113 ±0.0001 inches

(b) 5 decks

Explanation:

Given information

52 cards, thickness is 0.590 ±0.005 inches

Since this is thickness of all the cards, to get the thickness of a single card we divide the total thickness (plus uncertainty) by the number of cards hence

1 card=±= 0.0113461 ±0.000096 inches

Considering that thickness is given to 3 significant figures while uncertainty is to 1 significant figure, the final answer should also conform to these hence giving the first part of the answer to 3 significant figures while second part to 1 significant figure yields 0.0113 ±0.0001 inches

(b)

Considering that the cards have uncertainty of 0.0001 inches and the number of decks, n required to create uncertainty of 0.00002 inch is given by

We need 5 decks for the given uncertainty

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