Question

Carter measures a line to be 10.39 cm long. If the actual measurement is 10 cm, find Carter's relative error to the nearest hundredth.

Answer 1

To calculate Carter's relative error, we can use the formula for relative error, which is given by:

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

In this case, the measured value is 10.39 cm and the actual value is 10 cm.

1. **Calculate the absolute error:**

\[
|\text{Measured Value} - \text{Actual Value}| = |10.39 - 10| = |0.39| = 0.39 \text{ cm}
\]

2. **Calculate the relative error:**

\[
\text{Relative Error} = \frac{0.39}{10} = 0.039
\]

3. **Convert to percentage:**

To express the relative error as a percentage, multiply by 100:

\[
\text{Relative Error as a Percentage} = 0.039 \times 100 = 3.9\%
\]

4. **Rounding to the nearest hundredth:**

Since the relative error expressed as a percentage is \(3.90\%\), when rounded to the nearest hundredth, it is:

\[
\text{Relative Error} \approx 3.90\%
\]

Thus, Carter's relative error to the nearest hundredth is **3.90%**.