Chapter 2.3, Problem 32PP

Interpretation Introduction

Interpretation:

Percent errors in density by student B’s trials are to be calculated.

Concept introduction:

The values that are obtained after an experiment are called its measured value or experimental value. And the values already known for any physical quantity in literature is called its accepted value or true value. For accuracy of any measurement, accepted and experimental value is compared.

Error in any calculation is obtained by the formula as follows:

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

Answer to Problem 32PP

By student B,

Percent error in density of sucrose in first trial is: $11.949\%$.

Percent error in density of sucrose in second trial is: $5.660\%$.

Percent error in density of sucrose in third trial is: $8.8050\%$.

Explanation of Solution

Given information:

Accepted density value of sucrose is $1.59{\text{g/cm}}^{\text{3}}$, Errors in each of the 3 trial are $-0.19{\text{g/cm}}^{\text{3}}$, $0.09{\text{g/cm}}^{\text{3}}$ and $-0.14{\text{g/cm}}^{\text{3}}$ respectively.

Percent error is percentage of error with respect to accepted value. Percent error in any calculation is obtained by the formula as follows:

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

Substitute $1.59{\text{g/cm}}^{\text{3}}$ in accepted value and $-0.19{\text{g/cm}}^{\text{3}}$ in error in above equation.

$\begin{array}{c}\text{Percent error}=\frac{\left|-0.19{\text{g/cm}}^{\text{3}}\right|}{1.59{\text{g/cm}}^{\text{3}}}\times 100\\ =0.1194\times 100\\ =11.949\%\end{array}$

Percent error in density of sucrose in first trial is: $11.949\%$.

Substitute $1.59{\text{g/cm}}^{\text{3}}$ in accepted value and $0.09{\text{g/cm}}^{\text{3}}$ in error in above equation.

$\begin{array}{c}\text{Percent error}=\frac{\left|0.09{\text{g/cm}}^{\text{3}}\right|}{1.59{\text{g/cm}}^{\text{3}}}\times 100\\ =0.0566\times 100\\ =5.660\%\end{array}$

Percent error in density of sucrose in second trial is: $5.660\%$.

Substitute

$1.59{\text{g/cm}}^{\text{3}}$ in accepted value and $-0.14{\text{g/cm}}^{\text{3}}$ in error in above equation.

$\begin{array}{c}\text{Percent error}=\frac{\left|-0.14{\text{g/cm}}^{\text{3}}\right|}{1.59{\text{g/cm}}^{\text{3}}}\times 100\\ =0.08805\times 100\\ =8.8050\%\end{array}$

Percent error in density of sucrose in third trial is: $8.8050\%$.

Conclusion

By student B,

Percent error in density of sucrose in first trial is: $11.949\%$.

Percent error in density of sucrose in second trial is: $5.660\%$.

Percent error in density of sucrose in third trial is: $8.8050\%$.