first of all 1 cup is equal to eight fluid ounces. the ounces your scale measures are weight ounces, not fluid ounces. so you can't just swap those back and forth.
secondly, companies measure out their food by weight. when your cereal bag fills up at the factory, it's sitting on a weight trap that stops filling it at a certain weight. when companies send their food to be tested for nutritional information, they weigh it out and send it in. they put the volume [cup] measurements on the package because people seem to think volume measurements are easier to measure than popping something on a scale. somewhere on that box it likely says that it's measured by weight and contents may settle [ie get crushed up in transportation, thus making the volume measurement incorrect].
your cereal should have a 1oz by cup serving size. all cereals have a serving size of one ounce. granola tends to be about 1/4 cup and something puffy might be be 1 and 1/4 cups for that same ounce of cereal. most other cereals fall somewhere in between.
the bottom of the bag of cereal [the crushed up bits] tends to be heavier per cup. or if you like to think of it a different way, a one ounce portion of it will be less than a cup. the top perfect pieces might be one ounce and one cup at the same time, but most cups of cereal will not weigh an ounce. again, weight ounces here, not fluid ounces. if the cereal you poured today was pretty typical of how a bowl of your cereal looks, you have been eating two portions at a time.
-google first. ask questions later.