Question
Eric measures a line to be 6.79 in long. If the actual measurement is 7 in, find Eric's relative error to the nearest thousandth.
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Answered by
GPT-4o mini
To find Eric's relative error, we can use the formula for relative error:
\[
\text{Relative Error} = \frac{|\text{Measured Value} - \text{Actual Value}|}{|\text{Actual Value}|}
\]
In this case, the measured value is 6.79 inches, and the actual value is 7 inches.
First, we can calculate the absolute error:
\[
|\text{Measured Value} - \text{Actual Value}| = |6.79 - 7| = | -0.21| = 0.21
\]
Next, we compute the relative error:
\[
\text{Relative Error} = \frac{0.21}{7}
\]
Now, divide 0.21 by 7:
\[
\frac{0.21}{7} \approx 0.030
\]
Finally, to express the relative error as a decimal rounded to the nearest thousandth:
\[
\text{Relative Error} \approx 0.030
\]
Thus, Eric's relative error to the nearest thousandth is:
\[
\boxed{0.030}
\]
\[
\text{Relative Error} = \frac{|\text{Measured Value} - \text{Actual Value}|}{|\text{Actual Value}|}
\]
In this case, the measured value is 6.79 inches, and the actual value is 7 inches.
First, we can calculate the absolute error:
\[
|\text{Measured Value} - \text{Actual Value}| = |6.79 - 7| = | -0.21| = 0.21
\]
Next, we compute the relative error:
\[
\text{Relative Error} = \frac{0.21}{7}
\]
Now, divide 0.21 by 7:
\[
\frac{0.21}{7} \approx 0.030
\]
Finally, to express the relative error as a decimal rounded to the nearest thousandth:
\[
\text{Relative Error} \approx 0.030
\]
Thus, Eric's relative error to the nearest thousandth is:
\[
\boxed{0.030}
\]
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