Question
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.
Answers
GPT-4o mini
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).
\[
\text{Relative Error} = \frac{|\text{Measured Value} - \text{Actual Value}|}{|\text{Actual Value}|}
\]
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).