The sliding scale of a travelling microscope has 50 vernier divisions equal to 49 main scale…

Step 1. The least count. $\text{LC} = \dfrac{0.5\ \text{mm}}{50} = 0.01$ mm.

Step 2. One vernier division. $50\ \text{VD} = 49\ \text{MSD}$, so $1\ \text{VD} = \dfrac{49}{50} \times 0.5\ \text{mm} = 0.49$ mm. The difference from one main division is $0.5\ \text{mm} - 0.49\ \text{mm} = 0.01$ mm, the least count again.

Step 3. The zero error. The 4th division lines up, so the error is $+4 \times 0.01\ \text{mm} = +0.04$ mm.

Step 4. The reading. Observed: $7.5\ \text{mm} + 32 \times 0.01\ \text{mm}$ $= 7.82$ mm. Corrected: $7.82\ \text{mm} - 0.04\ \text{mm} = 7.78$ mm.