Question

Eric measures a line to be 7.54 cm long. If the actual measurement is 8 cm, 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 7.54 cm and the actual value is 8 cm.

First, we calculate the absolute error:

\[
\text{Absolute Error} = |\text{Measured Value} - \text{Actual Value}| = |7.54 - 8| = | -0.46| = 0.46
\]

Next, we plug the values into the relative error formula:

\[
\text{Relative Error} = \frac{0.46}{8}
\]

Calculating this gives:

\[
\text{Relative Error} = 0.0575
\]

To express the relative error to the nearest thousandth, we round 0.0575:

\[
\text{Relative Error (rounded)} = 0.058
\]

Thus, Eric's relative error to the nearest thousandth is **0.058**.