How to Calculate Price Elasticity of Demand When Perfectly Elastic?
$$\epsilon_D=\frac{\% \Delta Q_D}{\% \Delta P}$$
A perfectly elastic demand curve is horizontal, meaning we quantity demanded can change by any amount without changing price (any quantity can be sold at the price corresponding the vertical intercept). Hence, for any change in quantity, $\% \Delta P=0$. While we cannot strictly divide by zero, in the limit, the ratio is infinity.