(a) A person’s blood pressure is measured to be$\mathbf{120}\mathbf{\pm }\mathbf{2}\mathbf{}\mathbf{mm}\mathbf{}\mathbf{Hg}$. What is its percent uncertainty? (b) Assuming the same percent uncertainty, what is the uncertainty in a blood pressure measurement of 80 mm Hg?

Uncertainty as a percentage is just relative uncertainty multiplied by 100. The percent uncertainty likewise lacks units since it is a ratio of comparable values.

Given Data:

Consider the given data as below.

Blood pressure is measured to be $\mathrm{A}=120\pm 2\mathrm{mm}\mathrm{Hg}$.

The uncertainty of blood pressure is $\mathrm{\delta }\mathrm{A}=2\mathrm{mm}\mathrm{Hg}$.

The percentage uncertainty is defined by,

$$\begin{gathered} \mathrm{Percent}\mathrm{Uncertainty}=\frac{\mathrm{\delta A}}{\mathrm{A}}\times 100\% \\ =\frac{2\mathrm{mm}\mathrm{Hg}}{120\mathrm{mm}\mathrm{Hg}}\times 100\% \\ =1.67\% \\ :2.00\% \end{gathered}$$

Hence, the measured blood pressure has a percent uncertainty of 2.00%.

The percent uncertainty in measured blood pressure of 80 mm Hg.

The uncertainty in the blood pressure can be calculated as follows:

$\mathrm{Percent}\mathrm{Uncertainty}=\frac{\mathrm{\delta A}}{\mathrm{A}}\times 100\%$

Substitute known values in the above equation.

$$\begin{gathered} 1.67\%=\frac{\mathrm{\delta A}}{80\mathrm{mm}\mathrm{Hg}}\times 100\% \\ \mathrm{\delta A}=\frac{1.67\times 80}{100} \\ =1.336 \\ :1\mathrm{mm}\mathrm{Hg} \end{gathered}$$

Hence, the uncertainty in blood pressure is1 mm Hg.