A bench length of 2.5m is measured by a student as 2.55m . Find the percentage error in the student measurements

Okay, Duke, let's break this down.

The actual length of the bench is $L_{actual} = 2.5 \text{ m}$. The student's measured length is $L_{measured} = 2.55 \text{ m}$.

Step 1: Calculate the absolute error in the measurement. $\text{Absolute Error} = |L_{measured} - L_{actual}|$ $\text{Absolute Error} = |2.55 \text{ m} - 2.5 \text{ m}|$ $\text{Absolute Error} = 0.05 \text{ m}$

Step 2: Calculate the percentage error. $\text{Percentage Error} = \frac{\text{Absolute Error}}{L_{actual}} \times 100\%$ $\text{Percentage Error} = \frac{0.05 \text{ m}}{2.5 \text{ m}} \times 100\%$ $\text{Percentage Error} = 0.02 \times 100\%$ $\text{Percentage Error} = 2\%$

The percentage error in the student's measurement is $\boxed{2\%}$.