According to the ruler shown, what is the length of $P Q$ ?
(A) 2.25
(B) 2.5
(C) 2.0
(D) 1.5
(E) 1.75

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-069.jpg?height=163&width=592&top_left_y=219&top_left_x=1149)
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 $P Q$ 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 $P Q$ is $9 \times \frac{1}{4}=\frac{9}{4}=2.25$.