Question
David measures a line to be 10.3 in long. If the actual measurement is 10 in, find David's relative error to the nearest thousandth.
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Answered by
GPT-4o mini
To find the relative error, we can use the formula:
\[
\text{Relative Error} = \frac{|\text{Measured Value} - \text{Actual Value}|}{|\text{Actual Value}|}
\]
In this case, the measured value is \(10.3\) inches and the actual value is \(10\) inches.
First, we compute the absolute error:
\[
|\text{Measured Value} - \text{Actual Value}| = |10.3 - 10| = |0.3| = 0.3
\]
Next, we compute the relative error:
\[
\text{Relative Error} = \frac{0.3}{10} = 0.03
\]
To express this relative error as a decimal and then to the nearest thousandth:
\[
0.03
\]
Since we need to round to the nearest thousandth, it is already in the required format:
Thus, the relative error is \( \boxed{0.030} \).
\[
\text{Relative Error} = \frac{|\text{Measured Value} - \text{Actual Value}|}{|\text{Actual Value}|}
\]
In this case, the measured value is \(10.3\) inches and the actual value is \(10\) inches.
First, we compute the absolute error:
\[
|\text{Measured Value} - \text{Actual Value}| = |10.3 - 10| = |0.3| = 0.3
\]
Next, we compute the relative error:
\[
\text{Relative Error} = \frac{0.3}{10} = 0.03
\]
To express this relative error as a decimal and then to the nearest thousandth:
\[
0.03
\]
Since we need to round to the nearest thousandth, it is already in the required format:
Thus, the relative error is \( \boxed{0.030} \).
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