Chapter 2.3, Problem 49SSC

Interpretation Introduction

Interpretation:

The error and the percent error of the following measurement of length: $\text{76}\text{.48}\text{cm,}\text{76}\text{.47}\text{cm}\text{and}\text{76}\text{.59}\text{cm}$ needs to be determined if the actual length of the object is $\text{76}\text{.49}\text{cm}$.

Concept introduction:

The error associated with the experimental value is the difference of the experimental and accepted value.

$\text{Error}=\text{experimental}\text{value}-\text{accepted}\text{value}$

Percent error represents the error as the percentage of the accepted value.

$\text{Percent}\text{error}=\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\times 100$

Answer to Problem 49SSC

The error for the measurements $\text{76}\text{.48}\text{cm,}\text{76}\text{.47}\text{cm}\text{and}\text{76}\text{.59}\text{cm}$ are $-0.01$, $-0.02$ and $0.10$ respectively. Percent error for the measurements $\text{76}\text{.48}\text{cm,}\text{76}\text{.47}\text{cm}$ and $\text{76}\text{.59}\text{cm}$ are $0.01307\%$, $0.02615\%$ and $0.1307\%$ respectively.

Explanation of Solution

The accepted vale is $\text{76}\text{.49}\text{cm}$

Error and percent error for $\text{76}\text{.48}\text{cm}$ calculation is as follows:

$\begin{array}{c}\text{Error}\text{for 76}\text{.48}=\text{experimental value}-\text{accepted}\text{value}\\ =76.48-76.49\\ =-0.01\end{array}$

$\begin{array}{c}\text{Percent}\text{error}=\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\times 100\\ =\frac{\left|-0.01\right|}{76.49}\times 100\\ =0.01307\%\end{array}$

Error and percent error for $\text{76}\text{.48}\text{cm}$ calculation is as follows:

$\begin{array}{c}\text{Error}\text{for 76}\text{.48}=\text{experimental value}-\text{accepted}\text{value}\\ =76.47-76.49\\ =-0.02\end{array}$

$\begin{array}{c}\text{Percent}\text{error}=\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\times 100\\ =\frac{\left|-0.02\right|}{76.49}\times 100\\ =0.02615\%\end{array}$

Error and percent error for $\text{76}\text{.48}\text{cm}$ calculation is as follows:

$\begin{array}{c}\text{Error}\text{for 76}\text{.48}=\text{experimental value}-\text{accepted}\text{value}\\ =76.59-76.49\\ =0.10\end{array}$

$\begin{array}{c}\text{Percent}\text{error}=\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\times 100\\ =\frac{\left|0.10\right|}{76.49}\times 100\\ =0.1307\%\end{array}$

Conclusion

The error for the measurements $\text{76}\text{.48}\text{cm,}\text{76}\text{.47}\text{cm}\text{and}\text{76}\text{.59}\text{cm}$ are $-0.01$, $-0.02$ and $0.10$ respectively. Percent error for the measurements $\text{76}\text{.48}\text{cm,}\text{76}\text{.47}\text{cm}$ and $\text{76}\text{.59}\text{cm}$ are $0.01307\%$, $0.02615\%$ and $0.1307\%$ respectively.