Eric measures a line to be 7.94 in long. If the actual measurement is 8 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, Eric's measured value is 7.94 inches, and the actual value is 8 inches.

1. Calculate the absolute error:

\[ |\text{Measured Value} - \text{Actual Value}| = |7.94 - 8| = | -0.06| = 0.06 \]

2. Now, use the relative error formula:

\[ \text{Relative Error} = \frac{0.06}{8} \]

3. Calculate the relative error:

\[ \text{Relative Error} = 0.0075 \]

4. To express this as a decimal to the nearest thousandth:

0.0075 rounds to 0.008 when rounded to the nearest thousandth.

Thus, Eric's relative error is approximately 0.008.