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Name: Robert
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Question:
I am trying to understand percentages. I understand that it is a formula such as the part/whole x 100 gives me a percent answer, but if 100% is the whole value, how can I get 300%? Is this considered the percent change from the original value or would it be better explained as three times the original value?



Replies:
You raise an important issue that is flagrant in both scientific and non-scientific literature. It is absolutely necessary when expressing percentages, to specify the percentage of WHAT!! Example: If a salt doubles its solubility if the temperature is raised from 25C to 50C it is OK to say the solubility increases by 200% = 2 x 100/%, but without specifying that the basis of the percentage is the solubility at 25C., the 200% has no meaning. Unfortunately, in socially charged issues protagonists and antagonists often toss out percentages without specifying the basis of the percentage. An intentionally skewed example: "The population of the US has increased by 1000%." But what is the present population compared to -- the last census, or the estimated population in 1800? I refer you to the classic book "How to Lie with Statistics" by Darrell Huff for more subtle examples of the misuse of numbers.

Vince Calder


Robert,

100% means the whole value of reference. You cannot just have 100%. You must have 100% of something, or more often 100% of an amount. Less than 100% is less than that amount. More than 100% is more than that amount. 300% of $15.00 is (300/100)*($15.00)=$45.00. You cannot receive 300% of the $15.00 from the wallet that holds that original $15.00, but you can get it from a different source. You can get it from a bet at the racetrack. Odds of 3-to-1 mean that if you win, you will get 300% of the original bet as winnings. Of course, you will also get back your original bet money.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College



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