You have a set of calipers that can measure thicknesses of a few inches with an uncertainty of 0:005 inches. I mesure the thickn

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You have a set of calipers that can measure thicknesses of a few inches with an uncertainty of 0:005 inches. I mesure the thickn

ess of a deck of 52 cards and get 0.590 in: (a) If you now calculate the thickness of 1 card, what is my answer, including its uncertaintyb) 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?

Physics

1 answer:

Yuliya22 [3.3K] · Answer 1 · 2026-02-22T21:24:04+03:00

To address this issue, we will utilize the principles concerning the calculation of significant figures while considering tolerance levels. Additionally, we must ensure that the total significant digits in the final result does not exceed those of the given values:

PART A) The thickness of the collection of 52 cards is

$T = 0.590 \pm 0.005 in$

The thickness, t, of a single card can be:

$t = \frac{0.590}{52} \pm \frac{0.005}{52} in$

$t = 0.0113461\pm 0.000096 in$

For the 52 cards, the thickness has 3 significant figures and the associated uncertainty has 1 significant digit. Therefore,

the significant figures for one card's thickness and the uncertainty must also align at 3 and 1 respectively.

$t = 0.01134 \pm 0.005 in$

$t = 0.0113 \pm 0.0001 in$

Thus, the thickness of an individual card is $\mathbf {t = 0.0113 \pm 0.0001 in }$

PART B) The uncertainty for one card when measured using a single deck is 0.0001 inch.

The number of decks, n, needed to achieve an uncertainty of 0.00002 inch is

$n = \frac{0.0001}{0.00002}$

$n = 5$

Consequently, 5 decks are necessary to measure the thickness of a single card with a 0.00002 inch uncertainty.