Question

Eric measures a line to be 2.32 in long. If the actual measurement is 2 in, find Eric's relative error to the nearest thousandth.

Answer 1

To find Eric's relative error in the measurement, we first need to calculate the absolute error and then find the relative error.

1. **Calculate the Absolute Error**:
The absolute error is the difference between the measured value and the actual value.

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

Plugging in the values:

\[
\text{Absolute Error} = |2.32 - 2| = |0.32| = 0.32
\]

2. **Calculate the Relative Error**:
The relative error is the absolute error divided by the actual value.

\[
\text{Relative Error} = \frac{\text{Absolute Error}}{\text{Actual Value}}
\]

Now we can plug in the values:

\[
\text{Relative Error} = \frac{0.32}{2}
\]

Calculating that gives:

\[
\text{Relative Error} = 0.16
\]

3. **Convert to a more useful format**:
To express this as a fraction or a percentage, we typically keep the value as is for relative error unless explicitly asked for a percentage. As a decimal, it’s 0.16. But since the problem asks for relative error to the nearest thousandth:

\[
\text{Relative Error} = 0.160
\]

Thus, Eric's relative error to the nearest thousandth is **0.160**.