‘Percent’ can be confusing

By From page A6 | August 05, 2014

The letter by Mikal Saltveit published Friday, July 25, should have said that the increase in atmospheric carbon dioxide over the past 18 years is analogous to adding almost 7,000 people to the population of Davis, not 2.3 people. My hope in writing is to leave at least one person with a better understanding of math and climate change concerns.

If 6 ounces of beer in a glass is increased to 9 ounces, the result is 1.5 times the initial amount, the same as saying that half the initial amount was added. Such a change is widely referred to as a 50 percent increase while simultaneously being an extra 3 ounces.

If the number 0.06 is increased to 0.09, the extra 0.03 is similarly a 50 percent increase. If this same set of numbers is referred to as 6 percent changing to 9 percent, the increase is still 50 percent, while also being an extra 3 percent (trouble!). The latter might be stated as “3 percentage points” in an attempt to avoid the misinterpretation trap that caught the July 25 letter.

It is also misleading to think of “percent” as a substance like beer, or a unit of measure like ounces. The word “percent” means “divided by 100,” so 6 percent is exactly the same thing as 0.06.

“Percent” terminology makes ratios seem like adding and subtracting, a fallacy. A 50-percent increase followed by a 50-percent decrease does not lead back to the original number. Multiplying by 1.5, then taking away half of that result actually leads to three-quarters of the original number.

Carbon dioxide increased from 365 to 401 millionths of the atmosphere, simply 1.1 times as much, with no need to be confused by “percent.”

Math should not be treated as a toolbox of obscure procedures, analogous to speaking a foreign language from a phrase dictionary without practicing pronunciation and grammar. While we need words to communicate, math is not about words any more than French is about English, so reducing the usage of “percent” might be a key step toward fluency in math.

John Whitehead

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