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What is the Relative Uncertainty and Absolute Uncertainty? log (104 plusminus 3 / 8 plusminus 1)...

What is the Relative Uncertainty and Absolute Uncertainty?

log (104 plusminus 3 / 8 plusminus 1)

10^ (1.234 plusminus 0.001)

Math   Statistics-And-Probability   
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Answer #1

a)

log (104) = 2.0170333393

log(104 + 1.375) = 2.02273758763

log(104 - 1.375)= 2.01125317013

absolute certainty = max( 2.02273758763 - 2.0170333393 ,   2.0170333393 -2.01125317013)

= max( 0.00570424833 , 0.00578016917)

= 0.00578016917

relative uncertainty

= 0.00578016917/2.0170333393

= 0.00286567854

b)

10^1.234 = 17.1395730751

10^ 1.235 = 17.1790838716

10^1.233 = 17.1001531509

absolute uncertainty = max( 17.1395730751 - 17.1001531509 , 17.1790838716- 17.1395730751)

= max(0.0394199242, 0.0395107965)

= 0.0395107965

relative uncertainty

= 0.0395107965/ 17.1395730751

= 0.00230523807

= 2.3%

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