If the quanity demanded of soda decreases by 5 percent when the price of soda rises by 100 percent what is the price elasticity of demand for soda

Price elasticity of demand is calculated as the ratio of change in demand to the ratio of change in price. So if the demand changes - 5% when the price changes 100%, the PED = - 5% / 100% = - 0.05. Most good have a PED < 0, since demand typically decreases when the price is increased.