Question

Carter measures a line to be 9.3 cm long. If the actual measurement is 9 cm, find Carter's relative error to the nearest hundredth.

Answer 1

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

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

In this case, the measured value is 9.3 cm and the actual value is 9 cm.

1. Calculate the absolute error:
\[
|\text{Measured Value} - \text{Actual Value}| = |9.3 - 9| = |0.3| = 0.3
\]

2. Now, use the absolute error in the relative error formula:
\[
\text{Relative Error} = \frac{0.3}{9}
\]

3. Perform the division:
\[
\frac{0.3}{9} \approx 0.0333\ldots
\]

4. To express this relative error as a percentage, multiply by 100:
\[
\text{Relative Error} \times 100 \approx 0.0333 \times 100 \approx 3.33\%
\]

5. Finally, rounding to the nearest hundredth gives us:
\[
\text{Relative Error} \approx 3.33\%
\]

Thus, Carter's relative error is approximately **3.33%**.