Calculate the percentage uncertainty for the measurement 105.01 e 0.02.

Question

ScanSolve AI Tutor · Accepted Answer

The question for part B appears to be incomplete as it only provides a single measurement ( $105.01 \pm 0.02$ ) without specifying an operation or another measurement to combine it with, similar to parts A and Question 4.

Assuming the task is to "calculate" a property of this given measurement, we will calculate its percentage uncertainty, which is a common calculation for a single measurement.

Question 3 Part B:
Calculate the percentage uncertainty for the measurement $105.01 \pm 0.02$ .

Identify the mean value and the absolute uncertainty.
The given measurement is $x \pm \Delta x$ .
$x = 105.01$ $\Delta x = 0.02$
Calculate the relative uncertainty.
The relative uncertainty is the ratio of the absolute uncertainty to the mean value.
$\text{Relative Uncertainty} = \frac{\Delta x}{x}$ $\text{Relative Uncertainty} = \frac{0.02}{105.01}$ $\text{Relative Uncertainty} \approx 0.000190458$
Convert the relative uncertainty to percentage uncertainty.
To express the uncertainty as a percentage, multiply the relative uncertainty by $100\%$ .
$\text{Percentage Uncertainty} = \text{Relative Uncertainty} \times 100\%$ $\text{Percentage Uncertainty} = 0.000190458 \times 100\%$ $\text{Percentage Uncertainty} \approx 0.0190458\%$
Round the percentage uncertainty to an appropriate number of significant figures.
Since the absolute uncertainty (0.02) has one significant figure, it is common to round the percentage uncertainty to two significant figures.
$\text{Percentage Uncertainty} \approx 0.019\%$
The percentage uncertainty of the measurement $105.01 \pm 0.02$ is approximately $0.019\%$ .
$\boxed{0.019\%}$

Calculate the percentage uncertainty for the measurement 105.01 e 0.02.

Answer

Step-by-step solution

Identify the mean value and the absolute uncertainty.

Calculate the relative uncertainty.

Convert the relative uncertainty to percentage uncertainty.

Round the percentage uncertainty to an appropriate number of significant figures.

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