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.
