Sure, let’s go through the calculation of the percent error step-by-step:
1. Identify the known values:
- The accepted value for the density of aluminum is 2.70 g/cm³.
- The student's measured value for the density of aluminum is 2.85 g/cm³.
2. Understand the percent error formula:
The percent error is calculated using the formula:
[tex]\[
\text{Percent Error} = \left| \frac{\text{Experimental Value} - \text{Accepted Value}}{\text{Accepted Value}} \right| \times 100
\][/tex]
3. Insert the known values into the formula:
[tex]\[
\text{Percent Error} = \left| \frac{2.85 \, \text{g/cm}^3 - 2.70 \, \text{g/cm}^3}{2.70 \, \text{g/cm}^3} \right| \times 100
\][/tex]
4. Subtract the accepted value from the experimental value:
[tex]\[
2.85 \, \text{g/cm}^3 - 2.70 \, \text{g/cm}^3 = 0.15 \, \text{g/cm}^3
\][/tex]
5. Divide the difference by the accepted value:
[tex]\[
\frac{0.15 \, \text{g/cm}^3}{2.70 \, \text{g/cm}^3} = 0.0555555555555556
\][/tex]
6. Convert the fraction to a percentage by multiplying by 100:
[tex]\[
0.0555555555555556 \times 100 = 5.55555555555556
\][/tex]
7. Round to the appropriate significant figures:
Both the measurements given (2.85 and 2.70) have three significant figures. Therefore, the percent error should also be reported with three significant figures.
[tex]\[
\text{Percent Error} \approx 5.56\%
\][/tex]
So the student's percent error is approximately [tex]\( 5.56\% \)[/tex].
