You will gain mass by inhaling, but the reading on the scale won’t show any difference. That’s because the scale never actually measures your weight. It measures your weight plus the weight of the air above the scale. It’s just calibrated to show zero if there is nothing but air on top of it. (I.e. you are not standing on it).
Now when you stand on it, you are replacing some of the air with your body (which is heavier than air).
When you inhale, you are replacing some more of the ambient air, but this time only with air (which weighs the same).
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