# % of a % convention **URL:** \ **Category:** Factual Questions\ **Created:** [February 14, 2007, 6:01pm UTC](https://boards.straightdope.com/t/of-a-convention/392229 "2007-02-14T18:01:43Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![Carnacki](https://avatars.discourse-cdn.com/v4/letter/c/b5e925/32.png) [@Carnacki](https://boards.straightdope.com/u/Carnacki)\ **Post date:** [February 14, 2007, 6:01pm UTC](https://boards.straightdope.com/t/of-a-convention/392229/1 "2007-02-14T18:01:43Z")
My job involves looking at various car loan and lease rates, and I noticed a convention that I’m not sure applies generally to mathematics. Sometimes a loan program will have a discounted rate if certain criteria are met - i.e., a 6.25% rate will be reduced by .25%. Inevitably, the intent is a resulting rate of 6.00%. But I have a feeling that if I asked somebody, without context, “What is 6.25% reduced by .25%” the answer would be 6.234375% (i.e., 6.25\*.9975). Or maybe to use a real life example, if I said that, due to new data, the chance of rain predicted this morning at 50% just went up by 20%, would you understand there was a 70% or a 60% chance of rain? Is there a convention in math that dictates how to interpret x% +/- x%? Maybe this belongs in IMHO, not sure…figured I’d try here first. –KidScruffy ---
**Author:** ![Earl\_Snake-Hips\_Tucker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/earl_snake-hips_tucker/32/3269_2.png) [@Earl\_Snake-Hips\_Tucker](https://boards.straightdope.com/u/Earl_Snake-Hips_Tucker)\ **Post date:** [February 14, 2007, 6:29pm UTC](https://boards.straightdope.com/t/of-a-convention/392229/2 "2007-02-14T18:29:08Z")
If it’s not in the context of a math class, I infer that the examples you’ve cited are implied to be added, not multiplied. But that’s just me. I think the implied wording, and most people understand it as such is "by 0.25 percentage _points_. And so far as GQ, your question as phrased answers itself. You just use +/-. It keeps things simple. ---
**Author:** ![naita](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/naita/32/5862_2.png) [@naita](https://boards.straightdope.com/u/naita)\ **Post date:** [February 14, 2007, 6:30pm UTC](https://boards.straightdope.com/t/of-a-convention/392229/3 "2007-02-14T18:30:33Z")
[QUOTE=KidScruffy] My job involves looking at various car loan and lease rates, and I noticed a convention that I’m not sure applies generally to mathematics. Sometimes a loan program will have a discounted rate if certain criteria are met - i.e., a 6.25% rate will be reduced by .25%. Inevitably, the intent is a resulting rate of 6.00%. But I have a feeling that if I asked somebody, without context, “What is 6.25% reduced by .25%” the answer would be 6.234375% (i.e., 6.25\*.9975). Or maybe to use a real life example, if I said that, due to new data, the chance of rain predicted this morning at 50% just went up by 20%, would you understand there was a 70% or a 60% chance of rain? Is there a convention in math that dictates how to interpret x% +/- x%? Maybe this belongs in IMHO, not sure…figured I’d try here first. –KidScruffy [/QUOTE] x% +/- y% is properly equal to x% +/- (x \* y)/100 If you want the (x +/- y)% answer, y should be measured in [percentage points](http://en.wikipedia.org/wiki/Percentage_point) rather than %. In everyday language though you never know what is meant. Percentage points is a good bet in both your examples, but the second one **could** be refering to an actual 20% increase. ---
**Author:** ![Carnacki](https://avatars.discourse-cdn.com/v4/letter/c/b5e925/32.png) [@Carnacki](https://boards.straightdope.com/u/Carnacki)\ **Post date:** [February 14, 2007, 6:41pm UTC](https://boards.straightdope.com/t/of-a-convention/392229/4 "2007-02-14T18:41:33Z")
[QUOTE=naita] x% +/- y% is properly equal to x% +/- (x \* y)/100 If you want the (x +/- y)% answer, y should be measured in [percentage points](http://en.wikipedia.org/wiki/Percentage_point) rather than %. In everyday language though you never know what is meant. Percentage points is a good bet in both your examples, but the second one **could** be refering to an actual 20% increase. [/QUOTE] Thanks for the answers - I wasn’t familiar with using the phrase “percentage points” as a unit of measure, but that would certaintly clarify things. Presumably there’s no symbol or shorthand for “percentage point” as a unit of measure, since % is already taken…? ---
**Author:** ![muttrox](https://avatars.discourse-cdn.com/v4/letter/m/a8b319/32.png) [@muttrox](https://boards.straightdope.com/u/muttrox)\ **Post date:** [February 14, 2007, 8:07pm UTC](https://boards.straightdope.com/t/of-a-convention/392229/5 "2007-02-14T20:07:57Z")
It’s all good, as long as you are sure to explicitly state what you are taking a percent **of**. Normally, you don’t need this, it’s usually clear from context. But in your case, there are two valid interpretations, you just need to state which one is being used. ---
**Author:** ![desdinova](https://avatars.discourse-cdn.com/v4/letter/d/8baadc/32.png) [@desdinova](https://boards.straightdope.com/u/desdinova)\ **Post date:** [February 14, 2007, 8:11pm UTC](https://boards.straightdope.com/t/of-a-convention/392229/6 "2007-02-14T20:11:22Z")
[QUOTE=KidScruffy] Thanks for the answers - I wasn’t familiar with using the phrase “percentage points” as a unit of measure, but that would certaintly clarify things. Presumably there’s no symbol or shorthand for “percentage point” as a unit of measure, since % is already taken…? [/QUOTE] Another way of avoiding the confusion is the term “basis points.” One basis point is 1/100 of a percent point, or 0.01%. So if I told you “we’ll take 25 basis points off your 6.25% interest rate” then that means your rate is 6.00%. This term is primarily used in the finance industry, where it’s obviously very useful.