Question

What is the percent uncertainty in the measurement$\mathbf{5}\mathbf{.}\mathbf{48}\mathbf{\pm }\mathbf{0}\mathbf{.}\mathbf{25}\mathbf{m}$?

Short answer

The percent uncertainty in the measurement is $4.6\%$.

Step-by-step solution

Step 1. Percent uncertainty in the measurement

Percent uncertainty can be mathematically expressed as the ratio of the absolute value of uncertainty to the given measured value multiplied by 100.

Consider the measurement $7.42\pm 0.16\mathrm{m}$. The percent uncertainty in this measurement can be expressed as:

$\begin{array}{c}\mathrm{Percentuncertainty}=\frac{0.16\mathrm{m}}{7.42\mathrm{m}}\times 100\%\\ =2.16\%\end{array}$

Thus, the uncertainty in the given measurement is $2.16\%$.

Step 2. Calculation of percent uncertainty in the measurement 5.48±0.25m

The percent uncertainty in the given measurement is as follows:

$\begin{array}{c}\mathrm{Percentuncertainty}=\frac{0.25\mathrm{m}}{5.48\mathrm{m}}\times 100\%\\ =4.562\%\\ \approx 4.6\%\end{array}$

Thus, the uncertainty in the given measurement is $4.6\%$.