Both are precise, but in different contexts.
An ounce is a smaller measure so 6 oz has a greater absolute precision. On the other hand, 320 is accurate to 2 significant figures so 320 lbs has greater relative precision.
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What determines how precise a measurement is
It is precise if it is repeatable.
Is as exact as possible
tenth of a gram
The precise measurement is 5.7 mm for the first value and 3.6 m for the second value.