To solve this problem we will apply the concepts related to the calculation of significant figures under tolerance levels. We will also take into account that the number of significant digits at the end of an answer must not be greater than the number of significant digits of a number:
PART A) The thickness of the 52 cards is
[tex]T = 0.590 \pm 0.005 in[/tex]
The thickness, t, of 1 card can be:
[tex]t = \frac{0.590}{52} \pm \frac{0.005}{52} in[/tex]
[tex]t = 0.0113461\pm 0.000096 in[/tex]
The thickness of 52 cards has 3 significant figures and the uncertainty has 1 significant digit. So
the significant figures of the thickness of one card and the uncertainty should also be 3 and 1 respectively
[tex]t = 0.01134 \pm 0.005 in[/tex]
[tex]t = 0.0113 \pm 0.0001 in[/tex]
Therefore the thickness of one card is [tex]\mathbf {t = 0.0113 \pm 0.0001 in }[/tex]
PART B) One card has uncertainty of 0.0001 in if measured using 1 deck.
The number of decks, n, required to create the uncertainty of 0.00002 in is
[tex]n = \frac{0.0001}{0.00002}[/tex]
[tex]n = 5[/tex]
Therefore, 5 decks are required to measure the thickness of one card with an uncertainty of 0.00002 in
Calipers is a device used to measure the dimensions of an object.
Calipers is a device used to measure the dimensions of an object. The calipers is shown in the attached image below.
Given information-
The uncertainty of the calipers is 0.005 inches.
The thickness of the 52 cards measured by the calipers is 0.590 in.
As the thickness of the 52 card is 0.590 with uncertainty of 0.0050. Thus the thickness of the 52 card is,
[tex]t=0.590\pm0.005 \rm in[/tex]
Thus the thickness of the one card find by dividing the the thickness of 52 cards by 52. Thus,
[tex]t_1=\dfrac{0.590\pm0.005}{52} \\t_1=0.0113461\pm0.000096\rm in[/tex]
Hence the thickness of the one card is [tex]0.0114\pm0.0001\rm in[/tex] with significant figures.
Suppose the [tex]n[/tex] number of card need to measure to get the thickness of the 1 card with the uncertainty of the callers 0.00002 inches.
As the the thickness of one card is measured with the uncertainty of 0.0001 In. Thus,
[tex]n=\dfrac{0.0001}{0.00002} \\n=5[/tex]
Thus the number of decks need to measure to get the thickness of the 1 card with the uncertainty of the callers 0.00002 inches is 5.
Hence,
Learn more about the calipers here;
https://brainly.com/question/1395924
