In 3/8 time, there are three eighth notes in one measure. Since each measure is defined in terms of beats rather than weeks, it's important to clarify that "weeks" is not a typical measurement used in musical time signatures.
However, if you're looking to understand how many beats are in a measure, a measure of 3/8 time contains three beats, with each beat being an eighth note. If you were to convert musical measures to something like weeks conceptually, it would depend on how you define the relationship between measures and weeks, but musically, there are no weeks in a measure of 3/8 time.
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