Inconsistent language of the percentage system

[Twinbee]

Wikipedia does a pretty good job at explaining how different calculators treat percentage differently. For example Google or Excel will say:
50 + 10% = 50.1 ... (== 50 + (10/100))

...but Soulver or Microsoft Calculator will say:
50 + 10% = 55 ... (== 50 + (50*10/100))

I understand the motivations for both systems pretty well. The former is for consistency with mathematics generally, while the latter is surely the 'popular' way, (maybe somewhat unfortunately).

More than an explanation (since I know reasoning can be applied to both of the above systems), I'd like some opinions, since I'm making my own multi-line calculator - a very good one I might add. At the moment, I'm leaning towards the 50 + 10% = 55 system. But then there's stuff like this:

2+3+5+10% = 5.5
2+3+5+10% = 11

Unfortunately again, the second way is the popular one I think. If people type the question, 11 is what they'd expect right? Are we talking 70% of people, or maybe 50 or 90%?

How about:
2+3*4+10%

Would most people (we're talking average Jane Bloggs up to pro mathematician here) generally tend to read this as:

a: ((2+3)*4)+10%
...or...
b: (2+(3*4))+10%
...or...
c: 2+(3*(4+10%))
...or...
d: 2+((3*4)+10%)

Any advice would be appreciated. In the end, I value consistency with the rest of math's operator precedence rules, but I also (grudgingly) value what people actually use, as they'll be the judges of my software, not me.

 

[xts]

I never use percentage notation in conjunction with non-dimensioned numbers.
If you say: 10kg+10% it is obvious you mean 11kg. If you pay discounted price 25.50€-10% it is equally unambiguous to be 22.95€.
It is hard to say how would I interprete your example - I would probably try to get it from wider context, or just judged the text as not precise enough.

 

[mathman]

If something is ambiguous, clarification is in order. In the above examples, 50 can be either the number 50 or 50%.

 

[Twinbee]

I agree clarification should be used where there is possibility for confusion, but there has to be a default, at least for the calc I'm making, and we can't expect everyone to use brackets like we would.

Math already has default precedence for otherwise confusing things like 7+5*3^2, so maybe percent has a system too? In my last example above, I'm guessing answer <b> is the system most people would expect, but I can't be sure. Again any advice would be appreciated.

 

[HallsofIvy]

You cannot add a number and a percentage so, in my opinion, 50+ 10% can only mean "50%+ 10%" which would be 60%. Saying that 10% is the same as 0.1 only makes sense when you are talking about 10% of a particular number. To say that "50+ 10%= 50.1" only makes sense if you are assuming that that 10% means 10% of 1.

 

[Mute]

I don't think it's uncommon for the percentage symbol to be treated as a unit which happens to be dimensionless and equal to 1/100. The wikipedia article on percentage also takes this position. So, in the OP's first post I would have taken "50 + 10%" to mean "50 + 0.1".

So, if I were faced with an expression like 1+2+3+4%, I would take the "%" symbol to be a unit that is equal to 0.001, and so I would evaluate that expression as 1+2+3+0.004, unless I had some information to tell me that there is a context for the expression that requires a different interpretation.

 

[pmsrw3]

Personally, I think you're fighting a losing battle. No one knows what percent means in a calculator. New users are going to have to do some experiments or read the doco to figure it out.

 

[Twinbee]

You cannot add a number and a percentage so, in my opinion, 50+ 10% can only mean "50%+ 10%" which would be 60%.

Yes I agree, and I kinda wish that the public did too. But survey 1000 people and give them a choice between 50.1, 55 and 60% and I bet you'll find more than half of people would say the answer is 55% and not one of the other two. Despite its horrible consistency (with say * n% which does work like *0.01), it's also arguably the most practical.

Personally, I think you're fighting a losing battle. No one knows what percent means in a calculator. New users are going to have to do some experiments or read the doco to figure it out.

Far from trying to fight a battle about what users should do, I'm semi-reluctantly surrendering and saying, "Okay, we'll go with what the majority think it should be". But again, I don't have the statistics, hence my original post.

Maybe there's a site I can create a poll which will draw the most votes and also have the widest audience? I know that no perfect site exists, but I'm looking for the best one. Actually, though not ideal, maybe I could create a poll in my first post if the moderators permit.

I would take the "%" symbol to be a unit that is equal to 0.001

You mean 0.01.

 

[Mute]

You mean 0.01.

Yes, of course. Too bad I can't edit the post now to correct it.

 

[Twinbee]

We both have a reason to edit our posts. I'm sure Physicsforums.com used to let you do this, even for older posts. Fwiw, I vote we have the facility back.

 

[dalcde]

50+10%=55 doesn't make much sense. "Start with 50 and add 10% (and get 55)" does make sense, but the "add" doesn't really refer to arithmetic addition and the notation is a poor one.

 

[Twinbee]

Yes, I agree. In fact I've also thought of using another operator (instead of plus) for consistency.

However, in the end, I need to go with what the public are familiar with. Even with the more mathematically literate crowd who visits these forums, I'm sure 55 would have a chance of reaching the majority. I might just post a poll in a separate thread...

 

[BloodyFrozen]

You cannot add a number and a percentage so, in my opinion, 50+ 10% can only mean "50%+ 10%" which would be 60%. Saying that 10% is the same as 0.1 only makes sense when you are talking about 10% of a particular number. To say that "50+ 10%= 50.1" only makes sense if you are assuming that that 10% means 10% of 1.

Agreed

 

[hubewa]

You cannot add a number and a percentage so, in my opinion, 50+ 10% can only mean "50%+ 10%" which would be 60%.

Agreed. My opinion on this is that 10% is equivalent the decimal 0.1 so essentially, you're just adding 50 + 0.1 = 50.1. If you don't state 10% of what, then it should be the safest option that 10% refers to 0.1.

eg 50 + 10% * 50 = 55

 

[chiro]

The way I interpret things is that if a number is without units of any kind it is dimensionless and is just a number.

If it has units, then that's what it is in terms of those unit's.

If it has a percentage, treat it like the case with units and treat it as such.

One thing though if someone was to use a percentage, then like any unit it should be consistent and have some extra information of what it is in relation to. So instead of 5% it should be something like 5% of x. Maybe you could represent this as 5%(x), I don't know but it has to be relative to some other quantity, otherwise it would not make sense.

 

[Twinbee]

I agree with you all in terms of consistency, but try arguing with this little lot ;)
http://www.answers.com/plus+percent

 

[BloodyFrozen]

I agree with you all in terms of consistency, but try arguing with this little lot ;)
http://www.answers.com/plus+percent

Wow, look at that notation...Scary :P

 

[hubewa]

http://wiki.answers.com/Q/671.51_plus_5_percent_equals

Had a look at one of them. This one is quite terrible.

But then, this forum is for ppl who, at the very least, know what they are doing in the basics of notation (plus, minus, percentage), not putting anyone down, unlike wikianswers.

 

[dalcde]

"plus 5%" is not equal to "+5%".