Question

Bob measures a line to be 9.28 ft long. If the actual measurement is 9 ft, find Bob's relative error to the nearest thousandth.

Answer 1

To find Bob's relative error, we first need to calculate the error in his measurement and then express this error relative to the actual measurement.

1. **Calculate the error**:
\[
\text{Error} = \text{Measured value} - \text{Actual value} = 9.28 \text{ ft} - 9 \text{ ft} = 0.28 \text{ ft}
\]

2. **Calculate the relative error**:
Relative error is given by the formula:
\[
\text{Relative Error} = \frac{\text{Error}}{\text{Actual value}}
\]
Substituting the values we have:
\[
\text{Relative Error} = \frac{0.28 \text{ ft}}{9 \text{ ft}} \approx 0.0311111111
\]

3. **Convert to a percentage**:
To express the relative error as a percentage, we multiply by 100:
\[
\text{Relative Error (percent)} = 0.0311111111 \times 100 \approx 3.11111111\%
\]

4. **Round to the nearest thousandth**:
We round \(3.11111111\%\) to the nearest thousandth:
\[
\text{Rounded Relative Error} \approx 3.111\%
\]

So, Bob's relative error, to the nearest thousandth, is approximately **3.111%**.