Answer:
Explanation:
Given the equation:
[tex]\implies \dfrac{[9.8(\pm0.3)-2.31(\pm 0.01)]}{8.5(\pm0.6)}[/tex]
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 = [tex]\sqrt{(abs. uncertainty_{v_1})^2+(abs. uncertainty_{v_2})^2}[/tex]
absolute uncertainty = [tex]\sqrt{(0.3)^3 + (0.01)^2}[/tex]
= [tex]\sqrt{0.09 + 0.0001}[/tex]
= 0.300167
∴
[9.8(±0.3) - 2.31(±0.01)] = 7.49(±0.300167)
The division process now is:
[tex]\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)}[/tex]
Relative uncertainty = [tex]\dfrac{(\pm 0.300167)}{7.49}\times 100 \ , \ \dfrac{(\pm 0.6) }{8.5} \times 100[/tex]
Relative uncertainty = ±4.007565% , ±7.058824%
[tex]\text{Relative uncertainty} = \sqrt{(4.007565)^2+(7.058824)^2}[/tex]
[tex]\text{Relative uncertainty} = \sqrt{16.06057723+49.82699626}[/tex]
[tex]\text{Relative uncertainty} = \sqrt{65.88757349}[/tex]
[tex]\text{Relative uncertainty} = 8.117116[/tex]
≅ 8%
The algebraic value = [tex]\dfrac{7.49}{8.5}[/tex]
= 0.881176
≅ 0.88
The percentage of the relative uncertainty =[tex]\dfrac{\text{Absolute uncertainty }}{\text{calculated value} }\times 100[/tex]
By cross multiplying:
[tex]\text{Absolute uncertainty} (\%) = \dfrac{\text{relative uncertainty} \times \text{calculated value}}{100}[/tex]
[tex]\text{Absolute uncertainty} (\%) = \dfrac{8.117116\times 0.881176}{100}[/tex]
[tex]\text{Absolute uncertainty} (\%) = 0.0715260[/tex]
[tex]\mathbf{\text{Absolute uncertainty} (\%) \simeq 0.07}[/tex]
Finally:
[tex]\mathbf{\implies \dfrac{[9.8(\pm0.3)-2.31(\pm 0.01)]}{8.5(\pm0.6)}= 0.88 \pm (0.07) \pm 8\%}[/tex]
