Percent error is often expressed as the absolute value of...

Percent error is often expressed as the absolute value of the difference between the true value and the experimental value, divided by the true value: percent error $=\frac{\mid \text { true value }-\text { experimental value } \mid}{\mid \text { true value } \mid} \times 100 \%$ The vertical lines indicate absolute value. Calculate the percent error for the following measurements: (a) The density of alcohol (ethanol) is found to be $0.802 \mathrm{~g} / \mathrm{mL}$. (True value: $0.798 \mathrm{~g} / \mathrm{mL}$.) (b) The mass of gold in an earring is analyzed to be $0.837 \mathrm{~g}$. (True value: $0.864 \mathrm{~g}$.)

Percent error is often expressed as the absolute value of the difference between the true value and the experimental value, divided by the true value:
percent error $=\frac{\mid \text { true value }-\text { experimental value } \mid}{\mid \text { true value } \mid} \times 100 \%$
The vertical lines indicate absolute value. Calculate the percent error for the following measurements:
(a) The density of alcohol (ethanol) is found to be $0.802 \mathrm{~g} / \mathrm{mL}$. (True value: $0.798 \mathrm{~g} / \mathrm{mL}$.) (b) The mass of gold in an earring is analyzed to be $0.837 \mathrm{~g}$. (True value: $0.864 \mathrm{~g}$.)

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Key Concepts

Percent Error

Percent error is a quantitative measure of how much an experimental measurement deviates from the true value, expressed as a percentage. It provides a standardized way to compare the magnitude of errors across different measurements by relating the absolute difference to the true value, and then converting this ratio into a percentage.

Absolute Value

Absolute value denotes the magnitude of a number regardless of its sign. In the context of percent error, it is used to ensure that only the size of the error is considered, regardless of whether the experimental measurement exceeds or falls short of the true value.

Experimental Value

The experimental value is the measurement obtained from an experiment or observation. This value is compared with the accepted true value to assess the accuracy of the measurement and to calculate the percent error.

True Value

The true value is the accepted or correct value of the quantity being measured, typically obtained through highly controlled conditions or standard reference methods. It serves as the benchmark against which experimental measurements are evaluated to determine their accuracy.

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