Perform the calculations and determine the absolute and percent relative uncertainty. Express each answer with the correct number of signifi

Question

Perform the calculations and determine the absolute and percent relative uncertainty. Express each answer with the correct number of significant figures.

a. [9.8(±0.3)−2.31(±0.01)]8.5(±0.6)= __________
b. absolute uncertainty: __________
c. absolute uncertainty: _________
d. percent relative uncertainty: ___________

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RobertKer 2 weeks 2021-07-16T06:31:43+00:00 1 Answers 0 views 0

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    2021-07-16T06:33:05+00:00

    Answer:

    Explanation:

    Given the equation:

    \implies \dfrac{[9.8(\pm0.3)-2.31(\pm 0.01)]}{8.5(\pm0.6)}

    The absolute uncertainty in a measurement is the term used to describe the degree of inaccuracy.

    The first step is to determine the algebraic value on the numerator.

    Algebraic value = 9.8 – 231

    = 7.49

    The absolute uncertainty = \sqrt{(abs. uncertainty_{v_1})^2+(abs. uncertainty_{v_2})^2}

    absolute uncertainty = \sqrt{(0.3)^3 + (0.01)^2}

    = \sqrt{0.09 + 0.0001}

    = 0.300167

    [9.8(±0.3) – 2.31(±0.01)] = 7.49(±0.300167)

    The division process now is:

    \implies \dfrac{[9.8(\pm0.3)-2.31(\pm 0.01)]}{8.5(\pm0.6)}= \dfrac{7.49 (\pm 0.300167)}{8.5 (\pm0.6)}

    Relative uncertainty = \dfrac{(\pm 0.300167)}{7.49}\times 100  \ , \  \dfrac{(\pm 0.6) }{8.5} \times 100

    Relative uncertainty = ±4.007565% ,  ±7.058824%

    \text{Relative uncertainty} = \sqrt{(4.007565)^2+(7.058824)^2}

    \text{Relative uncertainty} = \sqrt{16.06057723+49.82699626}

    \text{Relative uncertainty} = \sqrt{65.88757349}

    \text{Relative uncertainty} = 8.117116

    ≅ 8%

    The algebraic value = \dfrac{7.49}{8.5}

    = 0.881176

    ≅ 0.88

    The percentage of the relative uncertainty =\dfrac{\text{Absolute uncertainty }}{\text{calculated value} }\times 100

    By cross multiplying:

    \text{Absolute uncertainty} (\%) = \dfrac{\text{relative uncertainty} \times \text{calculated value}}{100}

    \text{Absolute uncertainty} (\%) = \dfrac{8.117116\times 0.881176}{100}

    \text{Absolute uncertainty} (\%) = 0.0715260

    \mathbf{\text{Absolute uncertainty} (\%) \simeq 0.07}

    Finally:

    \mathbf{\implies \dfrac{[9.8(\pm0.3)-2.31(\pm 0.01)]}{8.5(\pm0.6)}= 0.88 \pm (0.07) \pm 8\%}

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