Question

Carter measures a line to be 7.19 ft long. If the actual measurement is 7 ft, find Carter's relative error to the nearest thousandth.

Answer 1

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

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

In this case:

- Measured Value = 7.19 ft
- Actual Value = 7 ft

Now, we can plug in the values:

\[
\text{Relative Error} = \frac{|7.19 - 7|}{|7|} = \frac{|0.19|}{7}
\]

Next, we calculate the fraction:

\[
\text{Relative Error} = \frac{0.19}{7} \approx 0.02714285714
\]

Now, we round this to the nearest thousandth:

\[
\text{Relative Error} \approx 0.027
\]

Thus, Carter's relative error is approximately **0.027**.