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.

Answer 1

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:

\[
\boxed{0.030}
\]