Question

What would be the uncertainty in volume delivered if the uncertainty in each reading were 0.03 mL? (Answer: 60.04 mL)

Short answer

The uncertainty in the volume delivered is $\pm 0.04\mathrm{mL}$.

Step-by-step solution

Defining uncertainty

Uncertainty refers to the inability to forecast a value. The last digit in a measured value will have a related uncertainty. Absolute and relative uncertainties are the two types of uncertainty.

Absolute ambiguity:

The marginal value of a measurement is expressed in this way.

Uncertainty in a relative sense:

It compares the extent of absolute uncertainty to the size of the measurement it is connected with.

Relative uncertainty $\mathrm{Relative}\mathrm{uncertainty}=\frac{\mathrm{absolute}\mathrm{uncertainty}}{\mathrm{magnitude}\mathrm{of}\mathrm{measurement}}$.

For a set of measurements having uncertainty values as ${\mathrm{e}}_1$,${\mathrm{e}}_2$, and ${\mathrm{e}}_3$, the uncertainty $\left({\mathrm{e}}_4\right)$in addition and subtraction can be calculated as follows:

${\mathrm{e}}_4=\sqrt{{\mathrm{e}}_1^2+{\mathrm{e}}_2^2+{\mathrm{e}}_3^2}$.

Calculating the uncertainty in the delivered volume

Given data:

Each reading has a degree of ambiguity of 0.03mL .

Uncertainty in volume:

Consider the following:

The initial reading is$0.05\left(\pm 0.03\right)\mathrm{mL}$.

The final reading is$17.88\left(\pm 0.03\right)\mathrm{mL}$.

The difference between these two variables is used to calculate the volume delivered:

$$\begin{gathered} 17.88\left(\pm 0.03\right) \\ \frac{-0.05\left(\pm 0.03\right)}{17.83\left(\pm \mathrm{e}\right)} \end{gathered}$$

The uncertainty (e) is calculated as follows:

$\begin{array}{l}e=\sqrt{{\left(0.03\right)}^2+{(0.03)}^2}\\ ==\sqrt{0.0018}\\ =0.042\end{array}$.

The uncertainty in the volume delivered is calculated by writing the resulting value in the significant figures as 0.04mL .

Thus, uncertainty in the volume delivered is calculated as $\pm 0.04\mathrm{mL}$.