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 $=\frac{ | \text { true value }-\text { experimental value } |}{\text { true value }} \times 100$ 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

Calculate the percent error for density of aluminum block

We are given the experimentally determined value of aluminum block's density as \(2.64 \frac{g}{cm^3}\) and the true value as \(2.70 \frac{g}{cm^3}\). Now, we will calculate the percent error using the formula: Percent Error \( = \frac {| true\,value - experimental\,value|}{true\,value} \times 100\) . Percent Error \(= \frac{ | 2.70 - 2.64 |}{2.70} \times 100 = \frac{0.06}{2.70} \times 100 = 2.22 \% \)

02

Calculate the percent error for iron determination in iron ore

We are given the experimental determination of iron in iron ore as \(16.48 \%\) and the true value as \(16.12 \% \). Now, we will calculate the percent error using the formula: Percent Error \( = \frac {| true\,value - experimental\,value|}{true\,value} \times 100 \). Percent Error \(= \frac{ | 16.12 - 16.48 |}{16.12} \times 100 = \frac{0.36}{16.12} \times 100 = 2.23 \% \)

03

Calculate the percent error for mass measurement using a balance

We are given that a balance measured the mass of a \(1.000g\) standard as \(0.9981g\). Now, we will calculate the percent error using the formula: Percent Error \( = \frac {| true\,value - experimental\,value|}{true\,value} \times 100 \). Percent Error \(= \frac{ | 1.000 - 0.9981 |}{1.000} \times 100 = \frac{0.0019}{1.000} \times 100 = 0.19 \% \) Now, we have calculated the percent error for each of the three measurements: a. The density of an aluminum block: \( 2.22\% \) b. The experimental determination of iron in iron ore: \( 2.23\% \) c. A balance measured the mass of a \(1.000g\) standard: \( 0.19\% \)

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