You have a set of calipers that can measure thicknesses of a few inches with an uncertainty of ± 0.005 inches. You measure the thickness of a deck of 52 cards and get 0.590 in:a. If you now calculate the thickness of 1 card, what is your answer, including its uncertainty? b. You can improve this result by measuring several decks together. If you want to know the thickness of 1 card with an uncertainty of only 0.00002 in., how many decks do you need to measure together?

a) x = (0.0114 ± 0.0001) in, b) the number of decks is 5

Explanation:

a) The thickness of the deck of cards (d) is measured and the thickness of a card (x) is calculated

x = d / 52

x = 0.590 / 52

x = 0.011346 in

Let's look for uncertainty

Δx = dx / dd Δd

Δx = 1/52 Δd

Δx = 1/52 0.005

Δx = 0.0001 in

The result of the calculation is

x = (0.0114 ± 0.0001) in

b) You want to reduce the error to Δx = 0.00002, the number of cards to be measured is

#_cards = n 52

The formula for thickness is

x = d / n 52

Uncertainty

Δx = 1 / n 52 Δd

n = 1/52 Δd / Δx

n = 1/52 0.005 / 0.00002

n = 4.8

Since the number of decks must be an integer the number of decks is 5