Percentage as Standard for Comparison
Date: 05/12/2003 at 13:42:05 From: Samantha Subject: More than 100%? How can you have more than 100% of something? 100% indicates you have a complete item, so how can it be more than complete?
Date: 05/12/2003 at 17:05:10 From: Doctor Peterson Subject: Re: More than 100%? Hi, Samantha. Good question! In some situations, a percentage refers to a part of all there is: I can't do more than 100% of a job, or eat more than 100% of the one pizza I ordered. More than 100% of the sky can't be covered by clouds, and more than 100% of the population can't be poor. But at other times, a percentage refers to something that is not an absolute limit, but just a standard for comparison. For example, the orange juice you drink in the morning may contain 100% of your daily requirement of vitamin C; if you eat any more foods containing vitamin C during the day, you will have eaten more than 100% of the RDA. For some vitamins, if you ate too much, it might be bad for you; however 130% in this case just means that you didn't need to have as much as you did, but it's okay to go beyond that. You've just taken in more than the recommended amount. As another example, you might plan to work 10 hours to put together a project. If you keep track of the time you've used, when you have spent 6 hours on it you will have used 60% of the planned time. But you might find that you aren't quite finished when the planned time is used up. If you spend 3 extra hours to make everything just right, making a total of 13 hours of work, you will have used 130% of the planned time. Now, if there had been only 10 hours left before the project was due, you couldn't have taken 130% of that time. But you had just PLANNED to use 10 hours, and it was possible (though possibly bad for your health, or your other activities) to use extra time for the project. Just like the vitamin C requirement, 100% didn't mean "all there is," but just "all we expect." The 130% means that you are "30% over budget." Do you see the difference in these two kinds of situations? The same thing happens with fractions. I can eat 1/2 a pizza, or 2/3 of a pizza; but I can also eat 2 3/4 pizzas, because the one pizza isn't all there is. I can fill 1/2 of my stomach, or 2/3 of my stomach, but not 2 3/4 stomachs, because I only have one. Fractions can be greater than 1, and percentages can be greater than 100. It's only when the fraction or percentage refers to a part of a whole that we can't go beyond the whole. Back to the nutrition label: a bag of potato chips can't be more than 100% fat, because the fat is PART of the chip, and the part can't be bigger than the whole. But it might conceivably have more than 100% of your daily requirement of fat, because the fat in the chips is only being COMPARED to the amount you're supposed to eat. Nothing prevents you from eating more. And finally, the number of calories you get from fat today can't be more than 100% of the total calories you consume, because they are part of that total. That gives us three different ways to express the fat in the chips as a percentage, and each percentage has a different meaning. Here's yet another way that a percentage can be used: A copier may have a setting for enlarging or reducing what you copy. The normal setting would be 100%, meaning that what comes out is the same size as what went in. You can set it to 50%, meaning the copy will be half the size of the original. Or, you can set it to 200%, and the copy will be twice as large. There's nothing wrong with that, because the copy is not part of the original; we are only comparing it to the original. And that's what makes the difference. Here is an old answer to a question like yours: More Than 100 Percent http://mathforum.org/library/drmath/view/58166.html If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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