David measures a line to be 10.3 in long. If the actual measurement is 10 in, find David's relative error to the nearest thousandth.

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 \(10.3\) inches and the actual value is \(10\) inches.

First, we compute the absolute error:

\[ |\text{Measured Value} - \text{Actual Value}| = |10.3 - 10| = |0.3| = 0.3 \]

Next, we compute the relative error:

\[ \text{Relative Error} = \frac{0.3}{10} = 0.03 \]

To express this relative error as a decimal and then to the nearest thousandth:

\[ 0.03 \]

Since we need to round to the nearest thousandth, it is already in the required format:

Thus, the relative error is \( \boxed{0.030} \).