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.