Question

Carter measures a line to be 5.8 cm long. If the actual measurement is 6 cm, find Carter's relative error to the nearest hundredth

Answer 1

To calculate Carter's relative error, we use the formula for relative error:

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

Where:
- Measured Value = 5.8 cm
- Actual Value = 6 cm

First, we find the absolute error:

\[
|\text{Measured Value} - \text{Actual Value}| = |5.8 - 6| = | -0.2 | = 0.2
\]

Next, we substitute this into the formula for relative error:

\[
\text{Relative Error} = \frac{0.2}{6}
\]

Calculating this gives:

\[
\text{Relative Error} = \frac{0.2}{6} \approx 0.0333\ldots
\]

To express this as a percentage, we multiply by 100:

\[
\text{Relative Error as Percentage} \approx 0.0333 \times 100 \approx 3.33\%
\]

Finally, rounding to the nearest hundredth, we find:

\[
\text{Relative Error} \approx 0.03 \text{ (as a decimal)}, \quad \text{or} \quad 3.33\% \text{ (as a percentage)}
\]

Thus, Carter's relative error is approximately **0.03** (or **3.33%**).