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In a lab, a group of students measured the temperature at which various substances boiled. Their results are listed in the table.

\begin{tabular}{|l|c|c|}
\hline
& Accepted Value (°C) & Measurement in Lab (°C) \\
\hline
seawater & 100.7 & 101.81 \\
\hline
mercury & 359.6 & 370.0 \\
\hline
jet fuel & 163.0 & 165.9 \\
\hline
ethanol (alcohol) & 78.4 & 81.8 \\
\hline
\end{tabular}

Which measurement has the highest percent error?

A. seawater
B. mercury
C. jet fuel
D. ethanol (alcohol)



Answer :

GinnyAnswer
To determine which measurement has the highest percent error, we need to follow these steps:

1. Calculate the percent error for each measurement. The formula for percent error is:

[tex]\[ \text{Percent Error} = \left( \frac{|\text{Measured Value} - \text{Accepted Value}|}{\text{Accepted Value}} \right) \times 100 \][/tex]

Let's calculate the percent error for each substance:

- Seawater:
[tex]\[ \text{Accepted Value} = 100.7 \quad \text{Measured Value} = 101.81 \][/tex]
[tex]\[ \text{Percent Error} = \left( \frac{|101.81 - 100.7|}{100.7} \right) \times 100 \approx 1.102 \% \][/tex]

- Mercury:
[tex]\[ \text{Accepted Value} = 359.6 \quad \text{Measured Value} = 370.0 \][/tex]
[tex]\[ \text{Percent Error} = \left( \frac{|370.0 - 359.6|}{359.6} \right) \times 100 \approx 2.892 \% \][/tex]

- Jet Fuel:
[tex]\[ \text{Accepted Value} = 1630 \quad \text{Measured Value} = 165.9 \][/tex]
[tex]\[ \text{Percent Error} = \left( \frac{|165.9 - 1630|}{1630} \right) \times 100 \approx 89.822 \% \][/tex]

- Ethanol:
[tex]\[ \text{Accepted Value} = 78.4 \quad \text{Measured Value} = 81.8 \][/tex]
[tex]\[ \text{Percent Error} = \left( \frac{|81.8 - 78.4|}{78.4} \right) \times 100 \approx 4.337 \% \][/tex]

2. Compare the percent errors to determine which one is the highest.

The calculated percent errors are:
- Seawater: approximately 1.102%
- Mercury: approximately 2.892%
- Jet Fuel: approximately 89.822%
- Ethanol: approximately 4.337%

From the calculated values, we can see that the percent error for Jet Fuel is the highest at approximately 89.822%.

Therefore, the measurement with the highest percent error corresponds to Jet Fuel.

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