Percentage points are the proper unit for the arithmetic difference of two percentages. Measurement is the determination of the size or magnitude of something. ... A percentage is a way of expressing a proportion, a ratio or a fraction as a whole number, by using 100 as the denominator. ...

Consider the following hypothetical example: in 1980, 40 percent of the population smoked, and in 1990 only 30 percent smoked. We can thus say that from 1980 to 1990, the incidence of smoking decreased by 10 percentage points. It would be misleading (and wrong) to say that smoking had decreased by 10 percent, since a percentage always indicates a ratio, not a difference. Indeed, given the above numbers, smoking decreased by 25 percent between 1980 and 1990.

Statements such as "between 1980 and 1990, the smoking rate decreased twice as much as the lung cancer rate" are ambiguous and should be avoided: it is not clear whether we are comparing percentages or percentage points here, and this makes a big difference.

Percentage points are often used to describe the change in interest rates or inflation rates. If an interest rate increases from 8 percent to 10 percent, then it increases by 2 percentage points. (One might also say that the interest rate has increased by 25 percent, but statements like this are fairly uncommon.) In this context, the simple "points" is often used instead of "percentage points". One hundredth of a percentage point is also known as a basis point. An interest rate is the price of money. ... Inflation, In economics, the inflation rate is the rate of increase of the average price level (a measure of inflation). ... A basis point (bp) is 0. ...

Percentage points are also used to express the difference of risks or probabilities. Consider for instance a certain drug, which cures a given disease in 60 percent of all cases; without the drug, the disease heals spontaneously in only 40 percent of cases. The drug thus causes an absolute risk reduction of 20 percentage points. Here the reciprocal is especially meaningful and is known as the number needed to treat (NNT): 1/.20 = 5; if you treat 5 patients with the drug, you can expect to heal one more case of the disease than you would have without using the drug. The word probability derives from the Latin probare (to prove, or to test). ... In mathematics, the reciprocal, or multiplicative inverse, of a number x is the number which, when multiplied by x, yields 1. ... The number needed to treat (NNT) is an epidemiological measure that indicates how many patients would require treatment with a form of medication to reduce the expected number of cases of a defined endpoint by one. ...