Question

David measures a line to be 3.87 ft long. If the actual measurement is 4 ft, find David's relative error to the nearest hundredth.

Answer 1

To find the relative error, we can use the formula:

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

In this case, the measured value is 3.87 ft and the actual value is 4 ft. Plugging these values into the formula, we get:

\[
\text{Relative Error} = \frac{|3.87 - 4|}{|4|}
\]

Calculating the absolute difference:

\[
|3.87 - 4| = |-0.13| = 0.13
\]

Now, divide this absolute difference by the actual value:

\[
\text{Relative Error} = \frac{0.13}{4}
\]

Calculating this gives:

\[
\text{Relative Error} = 0.0325
\]

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

\[
\text{Relative Error} \times 100 = 0.0325 \times 100 = 3.25\%
\]

To the nearest hundredth, the relative error is:

\[
\boxed{0.03}
\]

Thus, David's relative error, expressed as a decimal, is 0.03 (or 3.25% if expressed as a percentage).