Measuring the price of gasoline in dollars per quart, an economist calculates the price elasticity of demand to be 1. What would the price elasticity of demand be if the economist had chosen to measure the price in dollars per gallon?

the same

Explanation:

it doesn't matter what was the original price elasticity of demand that the economist calculated in the first place, but if he/she changes the metrics, it wouldn't change the answer at all.

Price elasticity of demand measures the percentage change in the quantity demanded of the product over the percentage change in the price of the product.

The percentage change is measured in %, not in dollars, gallons, quarts, pints, tons, inches, etc.