Question

Eric measures a line to be 2.12 cm long. If the actual measurement is 2 cm, find Eric's relative error to the nearest thousandth.

Answer 1

To find Eric's relative error, we first calculate the absolute error, which is the difference between the measured value and the actual value. Then, we calculate the relative error by dividing the absolute error by the actual value.

1. **Calculate the Absolute Error:**
\[
\text{Absolute Error} = \text{Measured Value} - \text{Actual Value}
\]
In this case:
\[
\text{Absolute Error} = 2.12 \, \text{cm} - 2.00 \, \text{cm} = 0.12 \, \text{cm}
\]

2. **Calculate the Relative Error:**
\[
\text{Relative Error} = \frac{\text{Absolute Error}}{\text{Actual Value}}
\]
Therefore:
\[
\text{Relative Error} = \frac{0.12 \, \text{cm}}{2.00 \, \text{cm}} = 0.06
\]

3. **Convert to Percentage (optional)**:
To express the relative error as a percentage, we multiply by 100:
\[
\text{Relative Error (percentage)} = 0.06 \times 100 = 6\%
\]

4. **Rounding to the Nearest Thousandth:**
Since the relative error itself is 0.06, and we express it in decimal form with three decimal places, we have:
\[
\text{Relative Error (to nearest thousandth)} = 0.060
\]

Thus, Eric's relative error, rounded to the nearest thousandth, is **0.060**.