First, make a simple syrup by combining the sugar and 1 cup water in a small saucepan and bringing to a boil on high heat, stirring frequently, until the sugar dissolves.
Let the syrup cool to room temperature before using.
(Store any leftover syrup, covered, in your refrigerator for up to 3 weeks.
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To make the daiquiri, combine the rhum, 1 ounce simple syrup, and the lime juice in a cocktail shaker.
Fill with ice and shake until very cold.
Strain into a cocktail glass and garnish with a lime round floating on top.
Serve.