Question

David measures a line to be 5.25 in long. If the actual measurement is 5 in, find David's relative error to the nearest thousandth.

Answer 1

To find David's relative error, we first need to calculate the absolute error and then use it to find the relative error.

1. **Calculate the absolute error**:
\[
\text{Absolute Error} = |\text{Measured Value} - \text{Actual Value}|
\]
Given that David measured 5.25 inches and the actual measurement is 5 inches, we have:
\[
\text{Absolute Error} = |5.25 - 5| = |0.25| = 0.25 \text{ inches}
\]

2. **Calculate the relative error**:
\[
\text{Relative Error} = \frac{\text{Absolute Error}}{\text{Actual Value}}
\]
Using the absolute error we calculated and the actual value (5 inches):
\[
\text{Relative Error} = \frac{0.25}{5}
\]

Performing the division:
\[
\text{Relative Error} = 0.05
\]

3. **Convert the relative error to a percentage** (if needed):
To express the relative error as a percentage, we multiply by 100:
\[
\text{Relative Error (percentage)} = 0.05 \times 100 = 5\%
\]

4. **Final Representation as a Decimal**:
Since you asked for the relative error to the nearest thousandth as a decimal, we write:
\[
\text{Relative Error} = 0.050
\]

Thus, David's relative error, to the nearest thousandth, is **0.050**.