A mercury barometer in a mountain village reads 685 mm…

Step 1. Pressure. $13\,600\ \text{kg/m}^3 \times 9.8\ \text{m/s}^2 \times 0.685\ \text{m} = 9.13 \times 10^{4}\ \text{Pa}$.

Step 2. Atmospheres. $\dfrac{9.13 \times 10^{4}\ \text{Pa}}{1.013 \times 10^{5}\ \text{Pa}} = 0.901\ \text{atm}$.

Step 3. Water. $\dfrac{9.13 \times 10^{4}\ \text{Pa}}{1000\ \text{kg/m}^3 \times 9.8\ \text{m/s}^2} = 9.32\ \text{m}$.