The accepted (true) density of aluminum is 2.70 g/cm3. If a student, after performing an experiment, found the value to be 2.45 g/cm3, calculate the percent error for this value. The accepted (true) density of aluminum is 2.70 g/cm3. If a student, after performing an experiment, found the value to be 2.45 g/cm3, calculate the percent error for this value. Group of answer choices ÂÂ
The Correct Answer and Explanation is :
To calculate the percent error, we use the following formula:
[
\text{Percent Error} = \left| \frac{\text{Experimental Value} – \text{True Value}}{\text{True Value}} \right| \times 100
]
In this case, the true (accepted) density of aluminum is given as 2.70 g/cm³, and the experimental density found by the student is 2.45 g/cm³.
Step 1: Find the difference between the experimental and true values.
[
\text{Difference} = 2.45 \, \text{g/cm}^3 – 2.70 \, \text{g/cm}^3 = -0.25 \, \text{g/cm}^3
]
Step 2: Take the absolute value of the difference.
[
\left| -0.25 \, \text{g/cm}^3 \right| = 0.25 \, \text{g/cm}^3
]
Step 3: Divide the difference by the true value.
[
\frac{0.25 \, \text{g/cm}^3}{2.70 \, \text{g/cm}^3} = 0.0926
]
Step 4: Multiply by 100 to get the percentage.
[
0.0926 \times 100 = 9.26\%
]
So, the percent error is 9.26%.
Explanation:
Percent error is a way of determining how close an experimental value is to the true or accepted value. In this case, the student found a density of 2.45 g/cm³ for aluminum, which is slightly lower than the accepted value of 2.70 g/cm³. The negative sign in the difference indicates that the experimental value is lower than the true value, but since percent error is always expressed as a positive value, we take the absolute value of the difference.
The formula used for percent error shows the relative size of the difference between the experimental and true values as a percentage of the true value. In this case, the difference is small relative to the true value (approximately 9.26%), indicating that the student’s experimental result is reasonably close to the true value, though not exact.
Percent error is important in scientific experiments because it helps to assess the precision of the measurements and whether any systematic errors may have affected the results. A larger percent error would indicate that the experimental value deviates significantly from the true value, while a smaller percent error indicates more accurate results.