Q14PE - College Physics (Urone)

Question

An infant’s pulse rate is measured to be $\mathbf{130}\mathbf{ }\mathbf{\pm }\mathbf{5}\mathbf{ }\mathbf{beats}\mathbf{/}\mathbf{min}$. What is the percent uncertainty in this measurement?

Step-by-Step Solution

Answer

The percentage uncertainty in the given case is  3.846%.

Step 1: Definition of percentage uncertainty

Percentage uncertainty implies the percentage of uncertainty in a given situation. Since it is a percentage, it has no units.

Step 2: Calculation of percentage uncertainty

Consider the given data as stated below.

An infant’s pulse rate is_-$\mathrm{A}=130 \mathrm{beats}/\min$.

The uncertainty, $\mathrm{\delta A}=5 \mathrm{beats}/\min$ .

The percentage of uncertainty is defined as follows:

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

Substitute $5 \mathrm{beats}/\min$ for $\mathrm{\delta A}$ and $130 \mathrm{beats}/\min$ for $\mathrm{A}$ in the above equation.

$$\begin{gathered} \mathrm{\delta A}\%=\frac{5 \mathrm{beats}/\min }{130 \mathrm{beats}/\min }\times 100\% \\ =3.846\% \end{gathered}$$

Step 3: Conclusion

Hence, the percentage uncertainty in the given case is 3.846%.