Chapter 1, Problem 6P

What is the percent uncertainly in the measurement 5.48 $\pm$ 0.25 m?

To determine

The percent uncertainty in the measurement 5.48 ± 0.25 m.

Answer to Problem 6P

Solution:4.6%

Explanation of Solution

Given:

5.48 ± 0.25 m is the measurement and we have to find its percent uncertainty.

Formula used:

Here, the formula used is −

  $\text{Percent uncertainty = }\frac{\text{Absolute uncertainty}}{\text{Absolute length}} \times 100 \%$

Calculation:

  $\begin{array}{l}\text{absolute uncertainty = 0}\text{.25}\hfill \\ \text{absolute length = 5}\text{.48}\hfill \end{array}$

  $\text{Percent uncertainty = }\frac{\text{Absolute uncertainty}}{\text{Absolute length}} \times 100 \%$

  $\begin{array}{l}\Rightarrow \frac{0.25}{5.48}\times 100\%\hfill \\ \Rightarrow 0.045620438\times 100\%\hfill \\ \begin{array}{l}\Rightarrow 4.5620438\%\\ \Rightarrow \approx 4.6\%\end{array}\hfill \end{array}$

Conclusion:

  $\text{Percent uncertainty in 5}\text{.48±0}\text{.25 m is 4}\text{.6\%}\text{.}$