Many times errors are expressed in terms of percentage. The percent error is the absolute value of the difference of the true value and the experimental value, divided by the true value, and multiplied by \(100 .\) Percent error \(=\frac{\mid \text { true value }-\text { experimental value } \mid}{\text { true value }} \times 100\) Calculate the percent error for the following measurements. a. The density of an aluminum block determined in an experiment was \(2.64 \mathrm{~g} / \mathrm{cm}^{3}\). (True value \(2.70 \mathrm{~g} / \mathrm{cm}^{3}\).) b. The experimental determination of iron in iron ore was \(16.48 \% .\) (True value \(16.12 \% .)\) c. A balance measured the mass of a \(1.000-\mathrm{g}\) standard as \(0.9981 \mathrm{~g}\)

Step by step solution

01

a. Calculate percent error for the aluminum block

For the aluminum block, the true value is given as \(2.70\mathrm{\:g}/\mathrm{cm}^3\), while the experimental value is given as \(2.64\mathrm{\:g}/\mathrm{cm}^3\). Using the formula for percent error: \(Percent\:error =\frac{|\text{true\:value}\:-\:\text{experimental\:value}|}{\mathrm{true\:value}} \times 100\) Plug in the true and experimental values and calculate the percent error: \(Percent\:error =\frac{|2.70\:-\:2.64|}{2.70} \times 100\) \(Percent\:error \approx 2.22\% \)

02

b. Calculate percent error for iron in iron ore

For the iron ore, the true value is given as \(16.12\%\), while the experimental value is given as \(16.48\%\). Using the formula for percent error: \(Percent\:error =\frac{|\text{true\:value}\:-\:\text{experimental\:value}|}{\mathrm{true\:value}} \times 100\) Plug in the true and experimental values and calculate the percent error: \(Percent\:error =\frac{|16.12\:-\:16.48|}{16.12} \times 100\) \(Percent\:error \approx 2.23\% \)

03

c. Calculate percent error for the mass of the 1.000-g standard

For the mass of the \(1.000\mathrm{\:g}\) standard, the true value is given as \(1.000\mathrm{\:g}\), while the experimental value is given as \(0.9981\mathrm{\:g}\). Using the formula for percent error: \(Percent\:error =\frac{|\text{true\:value}\:-\:\text{experimental\:value}|}{\mathrm{true\:value}} \times 100\) Plug in the true and experimental values and calculate the percent error: \(Percent\:error =\frac{|1.000\:-\:0.9981|}{1.000} \times 100\) \(Percent\:error \approx 0.19 \% \) To summarize, the percent errors for each scenario are as follows: a. Aluminum block: \(2.22\%\) b. Iron in iron ore: \(2.23\%\) c. Mass of the \(1.000\mathrm{\:g}\) standard: \(0.19\%\)

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