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In the formula NaBrO3, Oxygen will always have a -2 oxidation number. In this case the total number for oxygen in -6 because there are three oxygen atoms. Sodium will always have a +1 oxidation number therefore its total oxidation number is +1. The entire charge has to equal zero so taking what we have now: -6 and +1 we have a -5 left over. Therefore, Bromine must have a +5 oxidation number.

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