Chapter 3.1, Problem 3SP

Interpretation Introduction

Interpretation : The student’s percent error is to be calculated.

Concept Introduction :

The formula to calculate the percent error is:

  $\begin{array}{c}\text{percent error = }\frac{\left|\text{error}\right|}{\text{accepted}\text{value}}\text{×100\%}\\ \text{=}\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\text{×100\%}\end{array}$

Answer to Problem 3SP

The student’s percent error is $2\%$ .

Explanation of Solution

Error is the measurement of the difference between the experimental value and the accepted value.

The experimental value is $2.04\text{meters}$ .

The accepted value is $2.00\text{meters}$ .

The formula to calculate the percent error is:

  $\begin{array}{c}\text{percent error = }\frac{\left|\text{error}\right|}{\text{accepted}\text{value}}\text{×100\%}\\ \text{=}\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\text{×100\%}\end{array}$

To calculate the percent error, substitute the values in the above equation.

  $\begin{array}{c}\text{percent error = }\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\text{×100\%}\\ \text{=}\frac{\left|2.04\text{m}-2.00\text{m}\right|}{2.00}\times 100\%\\ =\frac{0.04\cancel{\text{m}}}{2.00\cancel{\text{m}}}\times 100\%\\ =2\%\end{array}$

Conclusion

The student’s percent error is $2\%$ .