, 2012

Solution 1

The segment of the ruler between each integer marking is divided into 4 equal pieces (that is, is divided into quarters).

Therefore, the point $Q$ is at $2 + \frac{3}{4}=2\frac{3}{4}$, and $P$ is at $\frac{2}{4}=\frac{1}{2}$.

Thus, the length of $PQ$ is $2\frac{3}{4} - \frac{1}{2} = \frac{11}{4} - \frac{2}{4} = \frac{9}{4}=2\frac{1}{4}$.

Writing this as a decimal, we obtain 2.25.

Solution 2

The segment of the ruler between each integer marking is divided into 4 equal pieces (that is, is divided into quarters).

There are 9 of these pieces between $P$ and $Q$.

Therefore, the length of $PQ$ is $9 \times \frac{1}{4} = \frac{9}{4}=2.25$.