4 oz of flour is about a half cup. Bakers routinely weigh their flour because it is more accurate then measuring with a cup. There are differences in weight, grind and moisture content that are better covered with actual weight, rather than depending upon volume.
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Volume measurements result in cups and weight measurements result in ounces and they are not the same. Common conversions indicate that four ounces of cake or pastry flour is equal to 1 cup. Different flours have different volumes to weight measurements so it is best to weigh substances to identify a weight value.