# How does a calculator percent key work?

Indeed, the inner workings of the “%” key on calculators is mysterious to many. Googled and found this Straight Dope entry, so I was hoping to finally know everything there is to know about that “%” key, but I am afraid, this article is really lacking and very misleading, if not plain wrong. For example:

By this logic: 400+27% should give us “400.27”, but it doesn’t. The article says:

Interestingly, when I do punch in 400+27% on my Casio, I get “695.89…”…

This calculator percent key article is in need of serious fixing…

Not so. The calculator is programmed to follow the Order of Operations, meaning that multiplication comes before addition.

The problem is more properly written as 400+(.27)400=X. The calculator is programmed to understand that 400 is the number that is the object of the percentage calculation.

.27 of 400 equals 108 (or 27 out of 100, which is the definition of 27%, times 4).

400+108=508

Now I’m wondering what you did to goof up like that.

I too wonder how I could “goof up” since I am not trying to explain anything myself, just pointing to errors in the entry

Anyway, let me try to explain more clearly: the entry is not just misleading but plain wrong, and I am demonstrating this with a simple example:

[ul]
[li] Entry states: “so if you type in 2%, it’ll calculate as .02”[/li][li] By this logic: “400 + 27%”, since “so if you type in 27%, it’ll calculate as .27”, should give me “400 + .27” which is “400.27”… Yes, I know that’s wrong, that’s the whole point! That’s just following what is (wrongly) stated in the entry.[/li][li] By the entry’s own statement: “400 + 27%” give “508”, which sounds right, but is it really? Did you check? Do whip out your El Cheapo calculator and give it a try:[/li][li] On my Casio DF-A200, punching in “400 + 27%” gives me “547.94…” (oops, I did goof up there. Probably a typo :smack: . I’ll fix that…) Note: I don’t know if different brand/models have different implementations of that “%” key, your results may vary, and here would be a good place to let us know [/li][/ul]

So: the entry logic is not consistent, neither within itself, nor with my experimental results. QED: the entry is broken, not what I am accustomed to coming from The Straight Dope…

FYI, that “547.94” is the amount that, if deducted 27% from, gives you 400.

No.

While it calculates the 27% as .27 for the purposes of multiplication, it is still using that number to evaluate a percentage. I’m uncertain as to how there could be any confusion about that. That is the decimal equivalent that the calculator uses to evaluate the percentage. That is what a percentage is, a fraction of a whole. Therefore, the percentage cannot be added to the whole without first evaluating it.

It doesn’t just go to 400+.27, it goes to 400+(.27)400.

Now, as far as calculators go, they’re pretty standard. I’ve tried it now on the computer, my TI-83+, and an el cheapo solar 8-digit job, and it’s come out the same every time. I don’t know what to tell you, pal.

Except that I can’t edit my post, re-oops I guess…

[ul]
[li]To get the 508 (400+27%) the entry mentions, on that same Casio DF-A200, I would punch in “400 X 27 % +”. Similarly, to get 292 (400-27%), I would punch in “400 X 27 % -”.[/li][li]Still on the same calculator, typing “400 - 27%” gives me “1381.48…”. Now I still don’ t have that one figured out yet… Any idea?[/li][/ul]

You know, I think you’re on to something. We’re not getting worse at math than the rest of the world, it’s the Japanese selling us faulty calculators that are making us THINK we’re dumb.

Heheh

Anyway, back on topic, we are onto something indeed. We have two main problems here: 1) wording of the article, and 2) innard workings of “%”, in particular with regards to “+” and “-” operations.

If you check what you wrote and what’s in the article, it is quite different. You make sense, but as far as I am concerned, the article does not. Let me quote it again:

This is at best misleading, and at worst, plain wrong. I would think this whole quote would be better left out. At first, I was thinking this could be rewritten somehow, but it is actually not that easy, since the behavior of the “%” key seems inconsistent according to the operation it is being combined with. That leads us to:

2) The innard workings of the “%” key

Well, it seems that things are not that simple after all, and should not be dismissed with a quick “Prefectly clear now, right?” (quote from the end of the entry).

We have already made clear that there are at least two radically different behaviors of the “%” key. When punching “400 + 27 %”, you get “508” (400 plus 27% of 400), but I get “547.94…” (somehow, that’s what you need if you want to get 400 substracting 27% from it).

I would guess that when you punch in “400 - 27 %”, you would get “292” (400 minus 27% of 400). Here, I am getting “1381.48…”. I have no idea where that latter number is coming from, and to tell you the truth, that’s what prompted my google session in the first place, and led me to this Straight Dope entry. Used the the quality of The Straight Dope articles, I thought that it would be where I’d find my answer, but I was sorely disappointed… So, how are “400”, “27”, “%” and “1381.48…” related? Anyone?

One important point: the behavior of the “%” key is inconsistant with regards to which operation it is combined to, even on your calculator. Following your previous post: punching in “400 + 27 %” is calculated as “400+(.27)400”… But then, think about it: if the behavior of “%” was consistant “400 X 27 %” should be calculated as “400 * (.27)400” and should give us “43200”, right? Of course it is not the case: “400 X 27 %” is calculated as just “(.27)400”. How is that consitent with the way things are calculated when “%” is combined with “+”? It just ain’t…

And finally, this brings us back to point 1): since the behavior of “%” is not consistent, you cannot just sum it up in a single quote without mentioning which operator it is combined to. Again, QED: that “Hitting the percent key tells the innards…” quote is wrong (misleading if you wish, but that ain’t much better…).
Aaaaanyhow… With all that, I am still wondering where that “1381.48…” is coming from…

I just found a pretty good page regarding the “%” key combined with “×” and “÷”. Still no info about that strange Japanese behavior with “+” and “-”. Still looking…

Looks like I am getting closer. According to this page , there seems to be at least 3 different implementations of the percent key:

[ul]
[li]Regular percent[/li][li]Profit margin percent[/li][li]Mark-up percent[/li][/ul]

One thing is sure, things are far from “perfectly clear now”

After some experimenting, it turns out that when I punch in “A - B %” on this Casio, what gets calculated is “100 * (A - B) / B”. So it is calculating the percentage increase from A to B. I guess that falls under the profit margin “%” key type. For example:

“450 - 400 %” gives “12.5”: it is a 12.5% increase from 400 to 450. If I sell \$450 something I bought \$400, I made a 12.5% profit margin.

“300 - 400 %” gives “-25”: it is a 25% decrease from 400 to 300.
and the obligatory:
“400 - 27 %”: so it is a 1381,48…% increase from 27 to 400!

Well, looks like these Japanese calculators ain’t broke after all

Just as a hijack, the idea of broken calculators is not necessarily just a joke. A few years back, I had someone with an HP calculator that was misprogrammed to do regressions (least squares.) I had assigned her some to do, and was spot checking, and she was always wrong. I went over with her what she was doing, and her calculator gave different results than mine. I went to the manual, we went through the “how to” exercise together, and I got the answer as per the manual, and her calculator didn’t. It must have been misprogrammed, and it was fairly subtle and sheer accident that we discovered it.

She should have sued HP for 0.99999983E+06 million dollars.

Oops again. Should fix that: turns out that the above percent increase is what is called markup percent (that I incorrectly called profit margin). So, to make things really clear:

``````

A: cost of purchase
B: sell price

markup percent = 100 * (B - A) / A
gross profit margin =  100 * (B - A) / B

``````

And so in the above example, profit margin was actually 11.11…%

Have you RTFM? You need a firm grasp of math to use a calculator, you know. .02 is the decimal equivalent of 2%. That’s why they seem to have corresponding numbers in the places you point out.

But from there your your logic (and math) break down: 400 +27% should not give us 400.27. It would yield 400 + (27 percent of 400) (which has already been determined to be 508). Based on this remark, I don’t think your understanding of math is strong enough support the position you are taking here. And I don’t think you are qualified to operate that calculator.