Eric measures a line to be 3.91 in long. If the actual measurement is 4 in, find Eric's relative error to the nearest hundredth.

Answer 1

To find Eric'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 \(3.91\) inches and the actual value is \(4\) inches.

1. Calculate the absolute error:

\[ |\text{Measured Value} - \text{Actual Value}| = |3.91 - 4| = |-0.09| = 0.09 \]

2. Now calculate the relative error:

\[ \text{Relative Error} = \frac{0.09}{4} \]

3. Perform the division:

\[ \frac{0.09}{4} = 0.0225 \]

4. Finally, to express the relative error as a percentage (which is common practice), multiply by 100:

\[ 0.0225 \times 100 = 2.25% \]

Thus, Eric's relative error, to the nearest hundredth, is \(0.0225\) (or \(2.25%\) when expressed as a percentage).