Question

Alex measures a line to be 4.66 cm long. If the actual measurement is 5 cm, find Alex's relative error to the nearest thousandth.

Answer 1

To find Alex'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 \(4.66 \, \text{cm}\) and the actual value is \(5 \, \text{cm}\).

1. Calculate the absolute error:

\[
|\text{Measured Value} - \text{Actual Value}| = |4.66 - 5| = | -0.34 | = 0.34
\]

2. Now, calculate the relative error:

\[
\text{Relative Error} = \frac{0.34}{5}
\]

3. Perform the division:

\[
\text{Relative Error} = 0.068
\]

4. Finally, to express this as a percentage (which is often what is needed for relative error), we multiply by 100:

\[
\text{Relative Error as a percentage} = 0.068 \times 100 = 6.8\%
\]

So, the relative error of Alex's measurement to the nearest thousandth (as a decimal) is:

\[
\text{Relative Error} = 0.068
\]

Thus, Alex's relative error, rounded to the nearest thousandth, is **0.068**.