A warning to engineers about calculators - Page 1
Forum section: electronics / general

author: Russ_A
author_rank: Contributor
timestamp: December 14, 2024, 03:34:24 pm
content: I decided to try a calculator app called Hiper Calc for Android.If you search for calculator app reviews it'll be there, highly recommended.At first I was very impressed by its ability to create user layouts. Really cool stuff. But within only a single day I uncovered several critical calculation flaws. For example, it has options for precision which are confusing. They seemed to be based on what size screen you were using. It turns out that whatever number of digits you choose to display, often 6 for readablity, is what the calculator would actually use in its calculations, which includes the ANS function (previous calculation result), stored values, etc. Crazy. So by making it a bit more readable on your phone you might only be using 4 or 5 digits in your calculations. And then I was testing its random number generator and it was completely flawed. It uses the same random number for all instances in a calculation, but then sometimes it doesn't, seemingly at random. And the last one I found was with its use of %. When typing an expression it'll put brackets around the number when you type in %, so you type 9 - 10 % and it'll have 9 - (10)% for the expression on the display. Seems great, right? What a good way to clarify what's going on. Wrong. That evaluates to 8.1. No kidding.I've been in contact with the developer and they're claiming that's the correct way of doing percentages.They just have no idea what they're doing. I explained that % should always be the same as /100 but they don't believe me. Note that this calculator allows full symbology and the entire expression to be entered at once before evaluating. This isn't some old school stepwise input. Anyway, my point is that in only a single day I've uncovered serious flaws with one of the seemingly best Android calculators out there. Please don't use a calculator that hasn't been through rigorous quality testing to do engineering calculations. I can imagine even a doctor or nurse screwing up a dosage because of the % flaw. It's crazy. So despite how cool that app is I guess I'll stick to using a handheld one that's been through the rigors of proper quality control and testing. As someone who does calculations for a living this has really put me off using apps.

author: jpanhalt
author_rank: Super Contributor
timestamp: December 14, 2024, 03:56:51 pm
content: What happens when you try (9 - 10)% or 9% -10%?Frankly, I rarely calculate with percent, and it's not completely clear what answer you wanted for 9 - 10% or 9- (10)%.

author: Squarewave
author_rank: Frequent Contributor
timestamp: December 14, 2024, 04:15:40 pm
content: That calculators days are numbered.

author: Russ_A
author_rank: Contributor
timestamp: December 14, 2024, 05:08:49 pm
content: My problem with it is that it's an amazing calculator. It let's you make your own layouts with the functions you want. It's damn-near perfect that way, which is why it's so popular. But being able to find such critical flaws in it in only a day is ridiculous. I'm sure I can find more. And the developer doesn't know what they're doing as far as calculations are concerned. The precision flaw is simply inexcusable. The percent calculation error, and their refusal to acknowledge it is crazy too. I never realized the risks of a dodgy app until today. It could cost someone serious money or make a serious mistake that could cause real harm. I now understand why there are calculator test suites. This obviously wouldn't come anywhere close to passing. I have two Casio fx-991EX calculators, one for home and one for work. I thought I could finally just use my phone because I found an app I loved. At least I know I can trust the Casio when I type a percent sign, and I know that it's storing fifteen or so digits in memory, not 4. Thank god the only thing the app might have thrown off for me is a drafting calculation or a voltage drop. I don't design bridges or medical devices.

author: golden_labels
author_rank: Super Contributor
timestamp: December 14, 2024, 05:12:21 pm
content: For the percent function the result is correct: 9 -10% = 9 - (9 * 10/100) = 9 - 0.9 = 8.1. I don’t recall it ever working otherwise. I also don’t see how it would work, given pocket, PoS, and office calculators do tail operations only.However, the warning holds in general. Given you emphasized the part about reviews: beyond calculators. Don’t trust those review systems. If anything, read only negative reviews and consider them only after carefully reading and evaluating.Even if the reviews were honest, and often they are not, the entire system can’t work. Consider, who posts those opinions. Those are completely random, anonymous people, under no obligation to express anything beyond their first emotional impression, in overwhelming majority lacking expertise to provide a reliable opinion and more often not having basic skills to conduct a test, and with the comment window too short to allow for a proper test anyway. I’ll also skip the entire topic of who runs those review systems.If you want an opinion, there is a lot of people doing honest, proper reviews. Dave is one of them. You know, who gives the opinion. You can judge their abilities, their knowledge and experience. You know their testing methods. Even somewhat entertainment(1)YouTube channels, like Project Farm, are worth orders more than any random opinions system.(1)I do respect the channel and that comment isn’t meant to belittle it. He does a great job. But some limitations, like being able to afford only a single specimen being tested, hamper the strength of the results. Some tests are also humorous and I believe this is intentional. Nothing wrong with that as long as one keeps that in mind. To be honest it would be detrimental to Project Farm, if tests were proper: it would then become a horrible, boring job.

author: jpanhalt
author_rank: Super Contributor
timestamp: December 14, 2024, 05:14:53 pm
content: It's still not clear what answer you expected.QuoteTo me, 9 -10% is 8.1. In the bolded sentence do you mean 8.1 is wrong? Or the answer given by the calculator was not 8.1?

author: TimFox
author_rank: Super Contributor
timestamp: December 14, 2024, 05:17:56 pm
content: Can it be set up to do RPN? That might avoid the problems reported here.

author: KE5FX
author_rank: Super Contributor
timestamp: December 14, 2024, 05:26:40 pm
content: The notion that calculation precision is the same as display precision, if true, is certainly a giant red flag.Personally I haven't touched a calculator since I foundJupyter QtConsole. If you assign a hotkey to bring it to the foreground at any time, it's no less convenient to use than a calculator. Great for people who like to work in consoles rather than full-fledged Jupyter notebooks.

author: wraper
author_rank: Unknown
timestamp: December 14, 2024, 05:41:20 pm
content: Quote from: golden_labels on December 14, 2024, 05:12:21 pmI'm not a calculator aficionado, but as I see it, the problem is 10% of what? Normally 10% should be converted to 0.1, usually to be used with multiplication.In windows standard calculator (% is absent in scientific) it happens just as op described when doing subtraction/addition. But if you do multiplication or division, it simply converts 10% to 0.1. My Casio fx-83ES converts it to 0.1 regardless of what you do. But with latter you enter a full expression rather doing a single operation with a known number.

author: tggzzz
author_rank: Super Contributor
timestamp: December 14, 2024, 05:43:35 pm
content: Quote from: KE5FX on December 14, 2024, 05:26:40 pmFor engineering, I agree - but other domains might well be different.The first place I would look for that is finance/accounting/insurance and similar. A big hint is that while there are many different types of rounding, bankers/accountants have their own mode requiring "round to nearest, ties to even". They get irritated with software that doesn't do that.

author: mqsaharan
author_rank: Regular Contributor
timestamp: December 14, 2024, 05:48:15 pm
content: Quote from: TimFox on December 14, 2024, 05:17:56 pmyes, it can.

author: wraper
author_rank: Unknown
timestamp: December 14, 2024, 05:48:41 pm
content: BTW google online calculator calculates 8.1 as well with entire expression entered.

author: Russ_A
author_rank: Contributor
timestamp: December 14, 2024, 05:51:40 pm
content: The calculator app I'm referring to shows full expressions, with symbology and everything. So yeah, % is just shorthand for divide by 100. It should have nothing whatsoever to do with anither term in the expression. The developer told me:Hi,The result is correct. If you add or subtract a percentage, it is always added or subtracted from some base. In your case it is subtracted 10% out of 9 which is 8.1.The operation that just divides the number of percents by 100 is totally useless.Best regards,JindřichAs you can see they have no idea how to evaluate a simple mathematical function. Type that into any full expression calculator, from programming languages, to Excel, to scientific calculators, to graphing calculators and % just means divide by 100. That the calculator automatically puts brackets around the term makes it even worse. I've attached some images that shows how it lets you input the function. It's beyond misleading, it's just wrong. It removes the blue brackets when you hit enter to evaluate the expression. I've attached screenshots.

author: wraper
author_rank: Unknown
timestamp: December 14, 2024, 05:55:03 pm
content: Quote from: Russ_A on December 14, 2024, 05:51:40 pmIf developer is wrong, google is wrong too. So I guess you need to prove google being wrong first before putting any blame to that developer.

author: Russ_A
author_rank: Contributor
timestamp: December 14, 2024, 05:57:00 pm
content: The problem is that it's misleading. You set 15 digits of precision in the settings but if at any point you change to fixed digit display while using the calculator you've lost your precision. Who would even program it that way? It's like they're using a string to store numbers for calculations rather than using a proper variable which goes through a format function when displayed onscreen.

author: Russ_A
author_rank: Contributor
timestamp: December 14, 2024, 05:59:49 pm
content: I thought I'd also point out the flaw with ran#, which outputs a random decimal between 0 and 1. Hitting enter over and over gives 0 some of the time and something else some of the time.

author: KE5FX
author_rank: Super Contributor
timestamp: December 14, 2024, 06:02:13 pm
content: Quote from: tggzzz on December 14, 2024, 05:43:35 pmSure, but rounding implies that there is precision beyond what's visible. Otherwise you're just truncating, right? To round the LSD up or down, you need at least one more digit beyond what you ultimately display.

author: Russ_A
author_rank: Contributor
timestamp: December 14, 2024, 06:13:35 pm
content: Yeah, a lot of calculators screw up %, but mot ones at this level of expression evaluation. This calculator shows stuff like I've attached below. It calculates % one way and then it changes its mind and does something else. And as I posted above the bracket thing is crazy. The calculator pretty much tells you that % is a function like any other and then it does some wild crap where it's doing the math differently. This is whackadoodle.

author: Russ_A
author_rank: Contributor
timestamp: December 14, 2024, 06:27:36 pm
content: I know I can't see the code but this reeks of using strings to store numbers. They just output the string to the display amd use the same thing in the calculations. That's not how a fancy graphing (yes, this app does graphing too) and scientific calculator should work or be expected to work. See the attachment. I've brought up the display option, which is a button on the calculator. If you choose fixed display it truncates the number and loses the precision you had. Now whether or not you agree or disagree with the things I found as soon as Instarted using the app ut's super obvious that whoever's programming this doesn't give a rat's ass about accurate calculations. They don't care and they feel it's not important because such a fundamental flaw is baked into the inmer workings of the program.

author: jpanhalt
author_rank: Super Contributor
timestamp: December 14, 2024, 07:04:28 pm
content: Quote from: Russ_A on December 14, 2024, 05:51:40 pmJudging from the number of people who thought the OP meant that result was wrong, perhaps this thread should be retitled: "A warning to engineers aboutcalculatorsEnglish."

author: coppice
author_rank: Super Contributor
timestamp: December 14, 2024, 07:06:52 pm
content: Quote from: Squarewave on December 14, 2024, 04:15:40 pmLike the 32nd of the month?I think accuracy really counts in a calculator. I mean you don't want to run an important calculation, and have the calculator do a number on you.

author: IanB
author_rank: Super Contributor
timestamp: December 14, 2024, 07:10:51 pm
content: Why do you title this thread "a warning about calculators", instead of "a warning about a specific phone calculator app I don't like"?

author: IanB
author_rank: Super Contributor
timestamp: December 14, 2024, 07:33:28 pm
content: Quote from: Russ_A on December 14, 2024, 03:34:24 pmI just did 9 - 10% on the iOS calculator and I got 8.1. I also did 9 - 10% on the HP 42s and got 8.1. Then I did it on the HP 35s and got 8.1.I would be very disappointed in any of these calculators if I didn't get the expected answer of 8.1.

author: Russ_A
author_rank: Contributor
timestamp: December 14, 2024, 07:58:38 pm
content: If you type 10% into a calculator and it results in 0.1 then you've taken 10% of what? It's gotta be ten per cent of 1, so 10/100*1 or just 10/100. If the calculator is designed to take 10% added or subtracted from some other term then 10% on its own shouldn't result in anything because 0+10% would be 0 and 1+10% would be 1.1 The % function should either require one parameter or two but not some random mix of both. 10% means 0.1. And the way this app shows brackets and weirdness around what it's actually doing is nuts. I think the developer is just grabbing function definitions off some website and chucking it into their app and not really understanding how it should work. And it results in this calculator doing the math differently than pretty much every physical scientific/graphing calculator out there. I've never seen a full expression calculator do it any other way. The ones that do stepwise calculations have a bit more leeway because they're using the full result of the previous calculation as one of the inputs to their % function. The app you showed is one of those, and yeah I do have a problem with the way the expression is shown onscreen by the end there. It's pretty much just displaying the order of button presses and not a proper formula.I've said I've only been using this a day and found significant problems with it in other areas so it's not just this one thing. They've implemented hundreds of functions and it wouldn't surprise me at all if there are other serious issues.

author: SteveThackery
author_rank: Super Contributor
timestamp: December 14, 2024, 08:09:50 pm
content: With great respect, I think @Russ_A's expectation might be in a minority. The Windows standard calculator and the Android one both give 8.1 as the answer to 9 - 10%.So far it looks like every calculator tested assumes "10% of 9" is what the user wants.Quote from: Russ_A on December 14, 2024, 07:58:38 pmHipercalc, the Android calculator and the Windows calculator all behave as described in bold.This is a fascinating thread - I had no idea about the loss of precision. Thanks, @Russ_A.

author: IanB
author_rank: Super Contributor
timestamp: December 14, 2024, 08:42:38 pm
content: Quote from: Russ_A on December 14, 2024, 07:58:38 pmIn this thread you have not demonstrated anything wrong with this calculator app. You have complained about a lot, but you have notdemonstratedit.None of your screenshots show the actual evidence of anything being wrong. And whatever you have shown with percentages is similar to every other calculator out there. We've compared with Google, iOS, Android, HP, and they all work in the same (logical, expected) way. I have tested with a Jot calculator from the dollar store, and I could test with Sharp, Casio and others. All work the same way.

author: SiliconWizard
author_rank: Super Contributor
timestamp: December 14, 2024, 08:50:50 pm
content: The % thing is a matter of convention and the OP may have been used to a particular calculator that was implementing it in a certain way. It's obviously not a matter of how the percentage is defined, but how a given calculator implements its "%" key in terms of syntax.The precision thing would be a more serious problem.I wouldn't recommend using any of those mobile apps for anything critiical anyway. For occasional quick calcs when you are on the go, that's fine.

author: Russ_A
author_rank: Contributor
timestamp: December 14, 2024, 08:53:17 pm
content: Those aren't calculators where you enter a long expression and then hit enter. They calculate each function one at a time, using the previous answer as an input to the new function. They essentially have a wildly different rule set for order of operations and I wouldn't expect the % function to behave the same as a proper modern scientific calculator. What this app developer has done is try to implement this full expression entry method when they don't understand it. They don't realize the distinction and they've tried to implement everything under the sun without any testing. They obviously don't test their functions because ran# is completely broken. They said they knew about it when I contacted them but that they didn't know how to fix it. My warning in general is just not to trust these things. It can look super polished on the surface but the programming can be a disaster.

author: IanB
author_rank: Super Contributor
timestamp: December 14, 2024, 08:55:24 pm
content: Quote from: SiliconWizard on December 14, 2024, 08:50:50 pmBut once again, there is a claim, but no demonstration of this in any screenshots. It may be true, but if so, why not illustrate the problem?Quote from: Russ_A on December 14, 2024, 06:27:36 pmExcept, in the screenshot provided, it does not truncate, it rounds, as would be expected. And there is no demonstration of the digits being lost. Why not?

author: ebastler
author_rank: Super Contributor
timestamp: December 14, 2024, 08:59:56 pm
content: Quote from: Russ_A on December 14, 2024, 08:53:17 pmCould you give us a few specific examples of calculator models whichdobehave the way you expect them to behave?

author: tggzzz
author_rank: Super Contributor
timestamp: December 14, 2024, 09:03:27 pm
content: Quote from: SiliconWizard on December 14, 2024, 08:50:50 pmThat calculator is relatively normal, at least with on the range of 1+2*3=9 or 1+2*3=7.If you want wierd, consider the Sumlock Anita 811, which is sometimes RPN and sometimes algebraic. Ish.https://www.eevblog.com/forum/buysellwanted/wtb-stand-for-early-fuller-calculator/msg5747661/#msg5747661And that didn't mention the full strangeness.

author: showman
author_rank: Contributor
timestamp: December 14, 2024, 09:21:08 pm
content: Quote from: IanB on December 14, 2024, 08:55:24 pmYeah, I tried that calculator and don't see any loss. Set the display precision to 3 decimal digits and did sin(45), got 0.707 and after that arcsin(Ans) gives 45.000 instead of 44.991. No problems with sqrt(2) sqrt(2)*Ans and 1/9 Ans*9 either.

author: iMo
author_rank: Super Contributor
timestamp: December 14, 2024, 09:58:21 pm
content: Quote from: Russ_A on December 14, 2024, 03:34:24 pmAfaik, all calculators I've ever seen understand the entering "9 - 10 %" as "please, subtract 10 percent from the 9".. This works that way since ever, imho.Creating something like "10%" producing "10/100" has absolutely none sense in any industry, imho.

author: Someone
author_rank: Super Contributor
timestamp: December 14, 2024, 10:03:27 pm
content: Quote from: ebastler on December 14, 2024, 08:59:56 pmTI CAS (nspire etc) evaluates the percent sign as /100 which produces:9 - 10% = 89/105 + 5 - 10% = 99/10anything which evaluates that second expression to something else has broken additions CommutativityandAssociativity, so by strict mathematical ordering the "correct" results for finance or smooth brains are nonsense and lack a clear ordering of operations.Quote from: iMo on December 14, 2024, 09:58:21 pmIndustry? depends on the specific industry. But what is the expected answer for 5 + 5 - 10% ? why should that be different to 5 - 10% + 5, or -10% + 5 + 5 ?

author: nfmax
author_rank: Super Contributor
timestamp: December 14, 2024, 10:14:41 pm
content: But % is a binary operator! It’s two arguments are the percentage itself, and the number you want to take the percentage of. It’s obvious in RPN

author: iMo
author_rank: Super Contributor
timestamp: December 14, 2024, 10:18:55 pm
content: This thread reminds me on an anecdotal situation - as a rookie in biz my boss called me saying "I told you to make 35% project margin thus you have to multiply your costs by 1.54"..

author: tggzzz
author_rank: Super Contributor
timestamp: December 14, 2024, 10:23:03 pm
content: Quote from: nfmax on December 14, 2024, 10:14:41 pmBut theneverythingis obvious (and simple) in RPN.Too many people seriously believe 1+2*3 is 9. But then some people believe -6 is larger than -4.

author: Someone
author_rank: Super Contributor
timestamp: December 14, 2024, 10:28:46 pm
content: Quote from: nfmax on December 14, 2024, 10:14:41 pmNot true in the mathematical sense:https://en.wikipedia.org/wiki/PercentageJust because there are calculators which use certain sequences to represent operations does not mean that maps 1:1 with written equations, RPN is pretty much the example of that. Percent is more like an SI prefix, all it says is this number next to it is in units of 1/100ths

author: Someone
author_rank: Super Contributor
timestamp: December 14, 2024, 10:32:42 pm
content: Quote from: tggzzz on December 14, 2024, 10:23:03 pmMore like RPN is unambiguous in operation order, a good thing. But it is not directly equivalent to:9 - 10%RPN would represent that as either:9 ENTER 10% -which is something else entirely, or as strictly mathematically written:1 enter 10% 9 - +/-(probably some better way to do that in RPN but I'm less familiar)

author: tggzzz
author_rank: Super Contributor
timestamp: December 14, 2024, 10:35:56 pm
content: My Anita 811 calculator has a "%=" key.What is "25% of 125" is calculated "C 125 * 25 %=" i.e. 31.25."If 21 is 25%, what is 100%" is calculated "C 21 / 25 %=" i.e. 84.

author: tggzzz
author_rank: Super Contributor
timestamp: December 14, 2024, 10:40:14 pm
content: Quote from: Someone on December 14, 2024, 10:32:42 pmNot quite.RPN associates operands and operator in a simple and predictable way that extends to complex calculations.Not entering keystrokes in the same order is unimportant and unsurprising. "If you want to go there , I wouldn't start from here"

author: iMo
author_rank: Super Contributor
timestamp: December 14, 2024, 10:42:03 pm
content: Quote from: Someone on December 14, 2024, 10:28:46 pmHmm, I doubt so. As I wrote above it would have no sense in any industry..Percentage on the calculator button pressed after a number P (like P %) says calculator to calculate P percent of the number A which you entered before the P..Like "A + P%" means A + A/100*P..For example entering "154 - 35 %" will be evaluated as 154 - 154/100*35 = 154 - 54 = 100

author: nfmax
author_rank: Super Contributor
timestamp: December 14, 2024, 10:42:55 pm
content: Quote from: Someone on December 14, 2024, 10:32:42 pmIt looks like the TI is treating % as a (postfix) unary operator, that divides its argument by 100. Perfectly reasonable, but not the same thing

author: Someone
author_rank: Super Contributor
timestamp: December 14, 2024, 10:47:20 pm
content: Quote from: tggzzz on December 14, 2024, 10:40:14 pmYou start with the assumption that 9 - 10% as written in clear text means 9 subtracting 10% of 9. Which I challenge anyone to find the strict mathematical definition of. While that might be slang/shorthand or accepted use in some fields, it does not make the numerical interpretation 9 minus 10 hundredths incorrect.The RPN method to calculate relied on the user translating that equation as written and where the error arises at (regardless of calculation method). Only if the equation was written in RPN to begin with would it be unambiguous.

author: tggzzz
author_rank: Super Contributor
timestamp: December 14, 2024, 10:57:10 pm
content: Quote from: Someone on December 14, 2024, 10:47:20 pmI don't assume anything.Writing it in RPNmakesit unambiguous.

author: Someone
author_rank: Super Contributor
timestamp: December 14, 2024, 10:58:33 pm
content: Quote from: nfmax on December 14, 2024, 10:42:55 pmSymbolic math calculator using strict mathematical rules? who'd have thought!"the same thing" is the point here neither calculator is "wrong" but the user has entered different intents from their reading of the question, it is about the interpretation of the equation as written:9 - 10%Using strict/formal/actual mathematical notation that has only one interpretation, 9 minus 10 hundredths.Quote from: nfmax on December 14, 2024, 10:14:41 pmOver to you for the references of where that is defined....Quote from: iMo on December 14, 2024, 10:42:03 pmLike I said, over to you to add some references for where % is defined in the language of mathematics as something other than a unary operator, and what rules it obeys in terms of order of operations and associativity.https://en.wikipedia.org/wiki/Associative_propertyYes, there are calculators which use % as a function to reduce effort/buttons/compelxity. But that does not make the written example of 9 - 10% change its language. You would need to define it as the sequence on a specific calculator being:9 enter 10 -+ %which is something different to9 - 10%9 - 10% can be entered on some calculators, directly as text. If that returns something other than 8.9 (or the 89/10 fractional result) then it is a failure of that calculator to follow standard mathematical (not slang) language.

author: showman
author_rank: Contributor
timestamp: December 14, 2024, 10:58:55 pm
content: RPN or no RPN is irrelevant, because it is still implementation specificon HP 42S the stack is not popped after "%", it is [9 0.9] after "9 10%" and "-" results in 8.1on HP 48G the stack is popped, so it is [0.9] after "9 10%" and "-" results in Error: Too few arguments

author: Someone
author_rank: Super Contributor
timestamp: December 14, 2024, 11:10:04 pm
content: Quote from: tggzzz on December 14, 2024, 10:57:10 pm9 - 10% is already unambiguous if you use the language of mathematics, just like your 1+2*3 example. Suggesting all equations are written down in RPN is plain silly.Your original claim is still incorrect:Quote from: tggzzz on December 14, 2024, 10:23:03 pmBecause clearly people are having trouble parsing either system. Changing from one language to another doesnt solve the underlying issue of mixing in slang terms and trying to accurately translate. And now we have user pointing out that RPN can have differing implementations (just as other calculator entry methods don't always agree on the details):Quote from: showman on December 14, 2024, 10:58:55 pm

author: IanB
author_rank: Super Contributor
timestamp: December 15, 2024, 01:49:38 am
content: First of all, calculators do not do mathematics, they do calculations. Calculators are designed to help you solve arithmetic problems in an efficient way.So trying to argue about the percent symbol from a mathematical point of view as being a unit of measure, as in parts per hundred, is to miss the point entirely. It is accurate, but is it useful?When doing practical calculations, % as an operator represents a ratio between two numbers. If I want to calculate 8.5% sales tax on goods priced at $45, I want so that sales tax = 8.5% of $45. And if I want the total price with tax added on, it ishelpfultocalculate$45 + 8.5% = $48.83, and do this efficiently with a minimum of keystrokes. This was accomplished readily by every calculator made since the 1980's.How is one going to do the "add sales tax" calculation efficiently on a device like the above-mentioned TI Nspire? I know, you will do something like (1 + 8.5%) * 45. But what the heck? I'm not going to waste my time doing that. I will just do 1.085 * 45 and be done with it.On the other hand, it doesn't matter much, because the Nspire is the wrong tool for the job. You are not going to carry an Nspire in your pocket to work out tax while shopping.

author: CatalinaWOW
author_rank: Super Contributor
timestamp: December 15, 2024, 03:34:22 am
content: Part of the confusion here is the dual use of the % symbol as both a unit signifier and an operator. A conversion from a percent display to a real number display involves the divide by 100 mentioned by the OP. But as an operator the result comes out as done by this and other calculators. On this subject the OP should just admit his error and move on.Few random numbers generators in calculators and even programs like Excel generate really good random numbers, but the report of the OP sound particularly bad. But demonstration is required which requires tediously writing down or exporting all of the results and analyzing them. It would only take a few dozen to see if the performance is as bad as reported. Many thousands to see if it is better than Excel.The calculation precision is easy to test. Set precision to 8 for example and enter a number 1.123456789 for example. The set precision to 1 and the multiply your number by 1. The set precision back to 8 and examine the result.Until something like this is reported I suspect operator error.

author: Halcyon
author_rank: Unknown
timestamp: December 15, 2024, 05:09:47 am
content: The Apple MacOS calculator also returns 8.1 for 9-10%.

author: Someone
author_rank: Super Contributor
timestamp: December 15, 2024, 05:27:15 am
content: Quote from: Halcyon on December 15, 2024, 05:09:47 amSure does, and then disagrees with the browser based calculator from Google on what the order of operations should be (while they both get 1+2x3=7). So there is no consistent agreement on what 5+5-10% actually means, and how the % sign should be interpreted in a written equation. Equally there is no well accepted definition of what the simpler 9-10% actually means without other context. The major error is calculators trying to smash together well defined mathematical operators with their (ill/poorly/non defined) percent function and writing them together as a single line. All this goes away if people accept that adjusting by percentages is wordy thing and has no agree/formal language in mathematical equations.10% less than the sum of 5 and 5parseable and fairly unambiguousThis is the way people who do maths as their profession see it:https://www.themathdoctors.org/order-of-operations-neglected-details/take % as a unary operator as discussed above.

author: IanB
author_rank: Super Contributor
timestamp: December 15, 2024, 06:15:19 am
content: Quote from: Someone on December 15, 2024, 05:27:15 amIndeed, and the corollary is that calculators are not puzzle solving devices, they are tools that can help you calculate things, provided you give precise instructions about what you want. If you write "5 + 5 − 10%", why should the machine have to read your mind and try to figure out what you mean by that? And why would you take a chance on the machine making the wrong guess? If you want the addition done first you can make that clear by writing instead "(5 + 5) − 10%" and then you will get what you need. And if you want it the other way, you can make sure of that too: "5 + (5 − 10%)".The general advice and feedback from mathematicians is to be clear and unambiguous in what you write, and that it never hurts to include parentheses for the avoidance of doubt.

author: Someone
author_rank: Super Contributor
timestamp: December 15, 2024, 07:33:20 am
content: Quote from: IanB on December 15, 2024, 06:15:19 amAgree, but I then take the hard stance of 9-10% = 8.9

author: IanB
author_rank: Super Contributor
timestamp: December 15, 2024, 08:10:40 am
content: Quote from: Someone on December 15, 2024, 07:33:20 amI think it depends on what is programmed into a device and what the user guide says. For example, with buttons on a calculator, it might be very clear that the percent key applies to the number on the display, and the function depends on what key is pressed before it. In user guide terms, the following sequence of key presses would be documented to produce the result 8.1:Code: [-]   [%] [=]When it comes to writing expressions in text in an edit window, it is more of a grey area, but it still depends on what the documentation says about how such expressions are treated. Unfortunately, I can't find any documentation for the Google calculator widget. So it's a matter of testing to find out.

author: SiliconWizard
author_rank: Super Contributor
timestamp: December 15, 2024, 08:29:18 am
content: Yeah." 9-10%" is going to be the new "8÷2(2+2)".

author: Kleinstein
author_rank: Super Contributor
timestamp: December 15, 2024, 08:39:29 am
content: For most calculators the % key is more of a joke, or for those who misses the decimal: it just divides the last number by 100. Form the math side this makes sense.The problem is more that one should not write 8 minus 10 % as 8-10%.

author: IanB
author_rank: Super Contributor
timestamp: December 15, 2024, 08:49:00 am
content: With an RPN calculator like the HP-42S, the behavior is much more clear and logical. For example:Code:y: 0.0000x: 0.0000 y: 9.0000x: 9.0000  [%]y: 9.0000x: 0.9000[−]y: 0.0000x: 8.1000You are not dealing with syntax or interpretation of expressions, you are dealing with operations that apply to the numbers on the display. What you see is what you get.

author: RFDx
author_rank: Regular Contributor
timestamp: December 15, 2024, 09:45:15 am
content: On my Casio FX-991DE plus:10% = 0.19 - 10% = 8.9which is obvious and what I, the user, am expecting.On Dreamcalc (PC calculator software), HiPER Calc Pro (Android calculator), Wolfram Alpha or most of the online calculators I tried:10% = 0.19 - 10% = 8.1This is just inconsistent if not silly.The scientific online calculator on desmos.com needs to be explicitly told the number to calculate a percentage off:9 - 10% of 9 = 8.19 - 10% of 1 = 8.9

author: IanB
author_rank: Super Contributor
timestamp: December 15, 2024, 10:11:04 am
content: Quote from: RFDx on December 15, 2024, 09:45:15 amOK, but which one is useless, and which one is useful?

author: tggzzz
author_rank: Super Contributor
timestamp: December 15, 2024, 10:16:01 am
content: Quote from: IanB on December 15, 2024, 06:15:19 amThe only thing I'll add is that people who throw numbers at a calculator and expect it to work out what they wanted, are also people that probably can't imagine there could be several interpretations of the keys they are entering.Shame people aren't taught to mentally calculate roughly what they expect the answer to be, and only then to use the calculator to verify the details. That applies toeverytool, e.g. DVM, scope, spectrum analyser etc.

author: tggzzz
author_rank: Super Contributor
timestamp: December 15, 2024, 10:17:58 am
content: Quote from: IanB on December 15, 2024, 10:11:04 amTheotherone, of course

author: Tation
author_rank: Regular Contributor
timestamp: December 15, 2024, 10:26:34 am
content: I only use RPN & RPL calculators, so for me % is a binary operator. Using % as /100 seems acceptable, even maybe coherent, but I think it is also less useful and even strange to mean Joe (9 * 5 % to compute the 5% of 9, that's clumsy, my TI Datamath II did it in the 70s, we are now on the XXI century). In any case, not a matter to rise a case over, provided that different calculator manufacturers & programmers have not reached a consensus on this.Hyper Calc performs calculations with the number P of digits you set (calls it precission, depends on portrait/landscape layout), and displays numbers with the number D of digits you set (must be D <= P). Five minutes using the app and one gets this. So, IMHO, this OP's rant was user error.

author: Tation
author_rank: Regular Contributor
timestamp: December 15, 2024, 10:50:44 am
content: IMHO, current calculators, that insist on you writing a complete algebraic expression to evaluate, like 5-1-2=, and then make great efforts to coerce any expression you write, no matter if it is ambiguous or not, into a number will do better rejecting ambiguous ones, forcing the user to write (5-1)-2= or 5-(1-2)=. Same can be said for programming languages.Or, of course, use the one and only true notation: RPN

author: RAPo
author_rank: Super Contributor
timestamp: December 15, 2024, 10:53:29 am
content: So true!Quote from: Tation on December 15, 2024, 10:50:44 am

author: m k
author_rank: Super Contributor
timestamp: December 15, 2024, 11:17:28 am
content: If I say 'ten minus ten percent' I mean that ten percent is off from ten.So 5 + 5 - 10% should be 9.I've never trusted calculators % calculations.Usually it seems to be 5 + 5 = a; a - a * 0.1 = result.Nine times five percent is 45%.

author: golden_labels
author_rank: Super Contributor
timestamp: December 15, 2024, 12:37:41 pm
content: If not talking about advanced scientific/engineering calculators, the precision was usually defined by the display width. Back to mechanic calculators. So is “strings” arithmetic: until recently virtually all simple calculators used BCD. That even transpired to early computers and is still available in the x86 instruction set.For those reasons I’d consider this an unexpected behavior caused by a clash between two different features: the fixed width arithmetic and width dynamically changed depending on screen orientation. Something to be addressed, that’s certain. But not as a plain bug, but behavior that may surprise the user.Of course using that representation in 21st century seems a weird choice for a tool that, I presume, aims to act as a scientific calculator. We have bignums and 64-bit floats, which suit those calculations much better. That I don’t deny. But it is not like the developers made some absurd, unheard of choice here.

author: golden_labels
author_rank: Super Contributor
timestamp: December 15, 2024, 12:52:45 pm
content: Perhaps it’s time for OP to simply admit the blunder?This thread becomes one of many, where a trivial issue receives pages of discussion, despite the subject got exhausted after a few posts.Quote from: RFDx on December 15, 2024, 09:45:15 amDid the meaning of word “inconsistent” change recently? All calculators consistently give 8.1. Yet you call them inconsistent, instead of the single one, which acts different…And this behavior is consistent with how the percent key on physical calculators usually worked,(1)and also how the percent sign is used in writing. “5 V ±10 %” is range[4.95, 5.05](corrected) [4.5, 5.5] V, not [4.9, 5.1] V. If you thought different… maybe it’s time to check all your designs?(1)And this is rooted in why the key is even present in calculators. In most it wouldn’t even be possible to use it in the way you suggest as “not silly.”

author: MK14
author_rank: Super Contributor
timestamp: December 15, 2024, 02:30:59 pm
content: This (online scientific calculator), gives 8.9https://www.calculator.net/scientific-calculator.html9 - 10% = 8.9But this one, and many (almost all other, online versions that I have tried so far), gives:https://web2.0calc.com/9 - 10% = 8.1 (this one also somewhat shows the individual calculation steps):

author: MK14
author_rank: Super Contributor
timestamp: December 15, 2024, 02:51:14 pm
content: I think, Subject to error, possible misremembering and confusion on my part.The (rather old now), physical calculators, especially 8 digit, simple/basic ones, but with a percentage key. Changed a '1', based on the percentage entered.E.g. 10% would create a 0.125% would make 0.25etc.So, relatively 'old' calculators (I haven't tested this theory out), would be 9 - 10% = 8.9But relatively modern calculators, would calculate it properly (as intended), and hence 9 - 10% = 8.1I.e. at some point in the past, when calculators became more powerful, the way percentages worked (on calculators), changed.Edit:The following article, seems to explain more about these calculator percentages. Such as why it works the way it does, and how the functionality is NOT necessarily the same, between major calculator manufacturer's.https://devblogs.microsoft.com/oldnewthing/20080110-00/?p=23853

author: RFDx
author_rank: Regular Contributor
timestamp: December 15, 2024, 03:28:10 pm
content: Quote from: golden_labelsNo. The Casio calculator shows 8.9, the correct value. 10% (or simply 10/100) is 0.1. Always.With the calculator apps the standalone value of 10% is 0.1 but changes suddenly to 0.9 when I subtract it from 9.Quote from: golden_labelsIs this some kind of alternative math I'm not aware of?

author: golden_labels
author_rank: Super Contributor
timestamp: December 15, 2024, 03:58:12 pm
content: If you want something actually unexpected: HMD’s model Nokia 225 4G. Guess what x % y returns. The “most obvious thing” of course: 100 · x / y.Quote from: RFDx on December 15, 2024, 03:28:10 pmThat’s one example, compared to multiple others you yourself have listed. All of which give the same, consistent behavior.Quote from: RFDx on December 15, 2024, 03:28:10 pmYes, all consistently give -10% · 9 being -0.9. All of them, you yourself said that.The other one is a different scenario, because percentage is not used in an expression. Strictly speaking percentage can’t be used without a reference value, but sometimes that reference is implied, so it may be convenient to have that kind of a conversion too.Quote from: golden_labelsNo, a misspelling typing an example quickly. The first range should be [4.5, 5.5]. Corrected.

author: xvr
author_rank: Frequent Contributor
timestamp: December 15, 2024, 05:23:53 pm
content: % operation here is a dual semantics operation, dependent of context. If you use it in expression of form<expr1> +/- <expr2>%it converted to<expr1> +% / -% <expr2>. (here +% and -% are defined as binary operation that add/subtracts <expr2> percents from <expr1>)In any other context it means multiplication to 0.01.Is it sounds logical? - Yes. Should it be implemented in this way?NO!And 2 pages of discussion here is an evidence of this.

author: golden_labels
author_rank: Super Contributor
timestamp: December 15, 2024, 06:33:50 pm
content: I wonder, how long such threads would be, if people did read earlier posts. Maybe half of the messages would be avoided, if anybody noticed their claims are already addressed earlier? Who knows, who knows…

author: jpanhalt
author_rank: Super Contributor
timestamp: December 15, 2024, 06:58:59 pm
content: Could you possibly mean warning about calculators that give the correct answer? That thread should be quite short, but then, maybe I missed the point.

author: Someone
author_rank: Super Contributor
timestamp: December 15, 2024, 08:51:06 pm
content: Quote from: golden_labels on December 15, 2024, 06:33:50 pmOh? like yourself?Quote from: golden_labels on December 15, 2024, 12:52:45 pma) there is not only a single example of % being interpreted as a unary operator as you claim here, but if you read the thread and the replies it is one example of many.b) 5V ±10% adds enough context for ambiguity to be removed, as the units of Volts is incompatible with unitless addition so the lack of units on the second value implies the % is dependent on something else. Contrast with "5V ±1% full scale" as a real world example.A calculator whichshows"9-10%" is showing two unitless numbers and a subtraction, no hint as to how that % should be interpreted. So it is not surprising that some different calculators interpret it differently. There is the commonly accepted consumer version, and the strict mathematical version, but what's missing from the consumer versions is clear documentation of what the operator is expected to do (still no one has provided reference to any mathematical rules of this consumer % operator).Which is completely different to whatever key sequence could be entered to calculate the different interpretations, after the user has made their own (as shown differing) interpretation.

author: IanB
author_rank: Super Contributor
timestamp: December 15, 2024, 09:50:17 pm
content: Quote from: Someone on December 15, 2024, 08:51:06 pmI don't think it's missing. I think it's a matter of reading the manual. For example, here is the user guide for a family of Casio calculators:

author: Someone
author_rank: Super Contributor
timestamp: December 15, 2024, 10:22:27 pm
content: Quote from: IanB on December 15, 2024, 09:50:17 pmYou're missing the distinction that is half of the "argument" people are throwing around.Pressing keys on a calculatoris not the sameas what's written.Is that example (of button sequences) from a calculator which shows a text representation on the screen? Does it show "9-10%" above/beside the result?Despite that I'm not sure some examples from a user guide fully explain how that % operator works and its rules. What happens when it is included in the middle of several operators? what is its precedence? how is unary vs binary decided? The argument is mostly about how do you take what can be readily done with some button sequences on a calculator and represent that unambiguously to the user. % always as unary with high precedence achieves that, but isn't what most people expect from the % operator.

author: IanB
author_rank: Super Contributor
timestamp: December 16, 2024, 12:42:47 am
content: Quote from: Someone on December 15, 2024, 10:22:27 pmYes, but I don't think there is any standard interpretation of the percent sign when writing text in a text window, other than the engineering interpretation of it being a unit of measure. In mathematical terms, 57% means the fraction 57/100 or 0.57. That's basically it.To go beyond that, you can look at the syntax of programming languages, which is usually specified with extreme precision. But in many programming languages, the % symbol is used as the modulo operator, nothing to do with percentages.In a calculator, the vendor is free to choose whatever behavior and meaning they wish, whatever they think is useful. As a user of a particular calculator you have to read the manual to find out how the % function works. And if you don't like the choice made by a particular vendor, you have to pick a different calculator. There are lots out there to choose from.

author: tggzzz
author_rank: Super Contributor
timestamp: December 16, 2024, 08:53:59 am
content: Quote from: IanB on December 16, 2024, 12:42:47 amThat's pretty much the case.I've already given examples of "non-standard" +,-,*,/,= keys. And, of course, there aretwointerpretations of 1+2*3 in common use.There are also many calculators that have functions important to specific industries. One variant of my calculator has "cosine squared" and "sine multiplied by cosine", which is apparently useful in surveying.

author: JPortici
author_rank: Super Contributor
timestamp: December 16, 2024, 09:24:24 am
content: Quote from: Russ_A on December 14, 2024, 03:34:24 pmit is! have you ever used the 4 operation + % calculators everybody except us uses (because we use scientific calculators)?

author: Tation
author_rank: Regular Contributor
timestamp: December 16, 2024, 09:38:05 am
content: I think that the final conclusion about "A warning to engineers about calculators" is: read the manual!

author: mikerj
author_rank: Super Contributor
timestamp: December 17, 2024, 09:38:39 pm
content: Quote from: RFDx on December 15, 2024, 03:28:10 pmNo, this is one possible interpretation of the sequence of inputs you provided. There is an alternative interpretation that is equally correct, as many examples in this thread have shown.

author: thm_w
author_rank: Super Contributor
timestamp: December 17, 2024, 10:32:51 pm
content: Quote from: m k on December 15, 2024, 11:17:28 amUse parenthesis if you want that result (5 + 5) - 10%English is not a good representation, "five plus five squared". Is that 5+52or (5+5)2? Who knows. Has to be written out or explained in extreme detail.

author: DimitriP
author_rank: Super Contributor
timestamp: December 17, 2024, 10:55:33 pm
content: Quote from: mikerj on December 17, 2024, 09:38:39 pmAlways follow manufacturers instructions.

author: Analog Kid
author_rank: Super Contributor
timestamp: December 18, 2024, 02:32:59 am
content: Quote from: tggzzz on December 14, 2024, 10:23:03 pm(1+2)*3 = 91+(2*3) = 7But then you must have known that you were posting an ambiguous expression, absent any stated rules of precedence. (I don't believe thereareany such implicit rules for an arbitrary expression posted on an Internet forum.)

author: themadhippy
author_rank: Super Contributor
timestamp: December 18, 2024, 02:41:23 am
content: Quotebodmas

author: Analog Kid
author_rank: Super Contributor
timestamp: December 18, 2024, 02:47:25 am
content: Never hoid of that before this.So "BODMAS" gets you 7 here.I'll have to remember that.

author: Andy Chee
author_rank: Super Contributor
timestamp: December 18, 2024, 02:52:54 am
content: I used to get these kind of videos in my YouTube recommendations algorithm, but now I no longer get these random math trivia in my recommendations anymore (from any creator, not just this one), even though my browsing has remained the same:

author: shabaz
author_rank: Frequent Contributor
timestamp: December 18, 2024, 03:49:32 am
content: Quote from: Andy Chee on December 18, 2024, 02:52:54 amInteresting video, but despite there being operator precedence rules, and despite that guy in the video possibly being right on a technicality (I'm not 100% sure; been ages since I studied maths, and maybe that fell under the 'Of' in BODMAS despite what Wikipedia says - no idea. From memory, I don't recall the 'Of' in BODMAS meaning what Wikipedia says it does, but I don't have a textbook at hand to know for sure), nevertheless, I think if anything he could only be right in an exam. I wouldn't trust him with an actual formula in real life, if he just assumed like that.In real life, there's a very high chance he would be wrong if he relied on that, because just seeing that ought to have made him question the actual intent of the person who wrote it. He shouldn't just assume that whoever wrote it like that, actually meant for the result to come out to what he believes it does.Ordinarily, just seeing something so intimate next to parenthesis makes one think if the author actually meant that portion to override, so it would be right to question it, or at least try out both ways, and see which one gives a value closer to what you estimate the result should be (i.e. rely on context and don't assume everyone will understand operator precedence rules or be perfect in their execution of them). There are plenty of mistakes in papers, one has to do a dry run with formulas with known input/output to see if it approximately agrees with reality, or if there's an error in the document.If I try that on my Casio calculator (fx-CG50), when I press EXE, it actually inserts extra parenthesis for me, giving the opposite result to what that guy in the video mentions is correct. And, intuitively, if I had seen that written, mentally I too would have assumed that author intended for the right side to be multiplied first too, i.e. I would have come up with a result of 1. (But I would have been aware thatpossiblythe result may be 16, i.e. time to now look beyond that and see which result actually makes sense, e.g. by looking elsewhere).

author: tggzzz
author_rank: Super Contributor
timestamp: December 18, 2024, 10:34:30 am
content: In response toQuote from: themadhippy on December 18, 2024, 02:41:23 amyou wroteQuote from: Analog Kid on December 18, 2024, 02:47:25 amNever been taught BODMAS or one of the equivalents?That illustrates how difficult it is to follow your suggestion "Math? Yes, obviously; but tailored to the student's level." in your posthttps://www.eevblog.com/forum/beginners/show-us-your-recommended-electronics-curriculum-for-beginners/msg5747835/#msg5747835It also helps us realise why you find Ebers-Moll a problem "(Please, please, no Ebers-Moll! that stuff gives me a headache.)" in your posthttps://www.eevblog.com/forum/beginners/show-us-your-recommended-electronics-curriculum-for-beginners/msg5747835/#msg5747835

author: RAPo
author_rank: Super Contributor
timestamp: December 18, 2024, 11:13:16 am
content: Ah it is a question of which rules are vouque.I've learned the old way, typing it in my HP calc (a HP41CX) gives me one.

author: tggzzz
author_rank: Super Contributor
timestamp: December 18, 2024, 12:11:13 pm
content: Quote from: RAPo on December 18, 2024, 11:13:16 amArithmetic rules of precedence are not a fashion accessory.Arithmetic operations have well-defined associative properties and commutative properties.https://en.wikipedia.org/wiki/Commutative_propertyhttps://en.wikipedia.org/wiki/Associative_propertyThe order of arithmetic operations follows from those.If you want to rewrite mathematics, be our guest. But make very sure you unambiguously state your rules and justify them.

author: RAPo
author_rank: Super Contributor
timestamp: December 18, 2024, 12:27:26 pm
content: I have a degree in math andpublished results.In the wikiorder of operationsthere is a special paragraph "Mixed division and multiplication" stating (bold is from my hand)There is no universal convention for interpreting an expression containing both division denoted by '÷' and multiplication denoted by '×'. Proposed conventions include assigning the operations equal precedence and evaluating them from left to right, or equivalently treating division as multiplication by the reciprocal and then evaluating in any order; evaluating all multiplications first followed by divisions from left to right; or eschewing such expressions and instead always disambiguating them by explicit parentheses.and a special text regarding precisely the 8:2(2+2):"Several commenters appear to be using a different (and more sophisticated) convention than the elementary PEMDAS convention I described in the article. In this more sophisticated convention, which is often used in algebra, implicit multiplication (also known as multiplication by juxtaposition) is given higher priority than explicit multiplication or explicit division (in which one explicitly writes operators like × * / or ÷). Under this more sophisticated convention, the implicit multiplication in 2(2 + 2) is given higher priority than the explicit division implied by the use of ÷. That’s a very reasonable convention, and I agree that the answer is 1 if we are using this sophisticated convention.I was referring to the maker of the video who stresses the words nowadays, modern interpretation.I' have no intend to rewrite mathematics.Maybethis articlewith the conclusionThe bottom line is that “order of operations” conventions are not universal truths in the same way that the sum of 2 and 2 is always 4. Conventions evolve throughout history in response to cultural and technological shifts. Meanwhile, those ranting online about gaps in U.S. math education and about the “right” answer to these intentionally ambiguous math problems might be, ironically, missing a bigger point.“To my mind,” says Grabiner, “the major deficit in U.S. math education is that people think math is about calculation and formulas and getting the one right answer, rather than being about exciting ideas that cut across all sorts of intellectual categories, clear and logical thinking, the power of abstraction and a language that lets you solve problems you’ve never seen before.” Even if that language, like any other, can be a bit ambiguous sometimes.is a valuable thing to readQuote from: tggzzz on December 18, 2024, 12:11:13 pm

author: tggzzz
author_rank: Super Contributor
timestamp: December 18, 2024, 01:24:05 pm
content: Quote from: RAPo on December 18, 2024, 12:27:26 pmI have a degree in electronics and several patents. I don't fall into the trap of thinking I know everything about electronics, nor that everything I write about electronics is correct.QuoteOf course that's not relevant to the example 1+2*3.QuoteWhat does the colon in "8:2(2+2)" mean?Of course that's not relevant to the example 1+2*3.QuoteThere's some truth there.Associative and commutative properties have been shown to be very useful and are accepted for arithmetic. That leads to BODMAS, which could equally well be written BOMDSA, but that acronym isn't as easy to say/remember.Nobody should fall into the trap of confusing computer languages with arithmetic; they have their own evaluation orders.For amusement, you could look at APL; athttps://tryapl.org/try typing in each of these expressions, and explain the results7 - 77 - 7 - 77 - 7 - 7 - 77 - 7 - 7 - 7 - 7

author: Analog Kid
author_rank: Super Contributor
timestamp: December 19, 2024, 12:13:20 am
content: Quote from: tggzzz on December 18, 2024, 10:34:30 amNope, never been taught that. How 'bout that?And I'm not going to bother answering the rest of your fucking scurrilous post.I believe what you did there is called "shooting the messenger", or poisoning the well, or some other well-known fraudulent argumentation technique.

author: Andy Chee
author_rank: Super Contributor
timestamp: December 19, 2024, 04:07:46 am
content: Quote from: tggzzz on December 18, 2024, 01:24:05 pmIn context, I think it's just a placeholder for the classical divide operator symbol (instead of slash), whose unicode I do not recall.

author: DimitriP
author_rank: Super Contributor
timestamp: December 19, 2024, 06:26:56 am
content: QuoteThat's T-Shirt worthy !!!As forQuote

author: IanB
author_rank: Super Contributor
timestamp: December 19, 2024, 07:15:05 am
content: Quote from: Analog Kid on December 19, 2024, 12:13:20 amJust in case anyone is baffled by differences between math and maths on each side of the pond, BODMAS in Britain is usually taught as PEMDAS in the USA.You have "Brackets, Orders, Division and Multiplication, Addition and Subtraction" vs "Parentheses, Exponents, Multiplication and Division, Addition and Subtraction".Though it has to be said this is usually applied in the context of algebra, when evaluating a formula such as:$$y=ax^2+bx+c$$It is fundamental that you evaluate \$x^2\$ before multiplying by \$a\$, and before adding \$bx\$ to this.Applying it to simple arithmetic is not really the point.

author: Analog Kid
author_rank: Super Contributor
timestamp: December 19, 2024, 07:24:30 am
content: I still have my algebra textbook (from college, not high school).Algebra and Trigonometry: A Functions Approach, Keedy & Bittinger, 1975I just had a look through it. Nothing, not a single word, about operator precedence, "BODMAS", "PEDMAS", none of that.

author: Mahagam
author_rank: Regular Contributor
timestamp: December 19, 2024, 09:41:54 am
content: The same application, the same expression. Just two different modes. And two different results. Where is my *trollface* smile icon?

author: tggzzz
author_rank: Super Contributor
timestamp: December 19, 2024, 10:44:08 am
content: Quote from: Analog Kid on December 19, 2024, 07:24:30 amI'm not surprised a university textbook doesn't mention operator precedence: it would be assumed that you had previously been taught it and understood it.We were taught that at 11yo, since it is a fundamental prerequsite for doing any and all basic algebraic manipulations. By basic I'm thinking of factorisation such as 3y2+12y = 3y(y+4)Discussing operator precedence in the context of the book's title would be like a university chemistry textbook discussing the difference between atoms, molecules, mixtures, compounds.

author: tggzzz
author_rank: Super Contributor
timestamp: December 19, 2024, 10:50:03 am
content: Quote from: Andy Chee on December 19, 2024, 04:07:46 amAh. Bizarre and unnecessary substitution.Makes me think of the way Humpty Dumpty used the symbol "glory" (which was, of course, written by the mathematician Lewis Carroll).

author: nigelwright7557
author_rank: Frequent Contributor
timestamp: December 19, 2024, 12:29:03 pm
content: Even the big boys get it wrong sometimes.I remember many years ago Intel had a calculation bug in a processor.If the answer was 65535 it gave answer -1.

author: MK14
author_rank: Super Contributor
timestamp: December 19, 2024, 12:51:32 pm
content: Quote from: nigelwright7557 on December 19, 2024, 12:29:03 pmI don't remember, any such bug. Unless you were referring to a divide bug, on the earliest Pentiums.65535 in (very old versions of) Excel, apparently can cause it to show the wrong value (100,000), found by me, using Search and/or AI (ChatGPT or similar).https://www.joelonsoftware.com/2007/09/26/explaining-the-excel-bug/

author: nfmax
author_rank: Super Contributor
timestamp: December 19, 2024, 01:12:02 pm
content: The warning to engineers must surely be: ‘Know Your Tools’. A calculators is a tool like any other. Check, don’t assume

author: RAPo
author_rank: Super Contributor
timestamp: December 19, 2024, 02:01:27 pm
content: I think Nigel was referring tothe FDIV bug.in the Pentium processor.65535<->-1 is indeed more excel like.Quote from: MK14 on December 19, 2024, 12:51:32 pm

author: tggzzz
author_rank: Super Contributor
timestamp: December 19, 2024, 02:41:24 pm
content: Quote from: nfmax on December 19, 2024, 01:12:02 pmJust so.A variant of that (one of the two mottos that I think are worth repeating) is "trust, but verify".Applies to non-engineers too, but engineers don't have an excuse

author: Analog Kid
author_rank: Super Contributor
timestamp: December 19, 2024, 08:57:30 pm
content: Quote from: tggzzz on December 19, 2024, 10:44:08 amWell, I can assure you that the topic never came up in high-school algebra class either. (I took the college course as a refresher.) Maybe things are different over there in the UK.

author: tggzzz
author_rank: Super Contributor
timestamp: December 19, 2024, 09:07:42 pm
content: Quote from: Analog Kid on December 19, 2024, 08:57:30 pmIf it wasn't taught, how could you proceed to understand and then do factorisation?

author: Analog Kid
author_rank: Super Contributor
timestamp: December 19, 2024, 09:16:31 pm
content: Quote from: tggzzz on December 19, 2024, 09:07:42 pmWellll, it was quite a fewyearsdecades ago, so memory is a little fuzzy: I'm guessing we were taught to do multiplication and division before addition and subtraction, but I think that was about it. Never heard any mnemonics like BODMAS back then. (Would have been helpful for sure, like "Roy G. Biv" which I do remember from back then.)

author: themadhippy
author_rank: Super Contributor
timestamp: December 19, 2024, 11:27:51 pm
content: Quotewe had it drummed into us around the same time we learned that some old horses can always hear there owners approach

author: IanB
author_rank: Super Contributor
timestamp: December 19, 2024, 11:55:14 pm
content: Quote from: Analog Kid on December 19, 2024, 09:16:31 pmYeah, it was quite a few decades ago for me too, and I don't remember any mnemonics at that time either. BODMAS, PEMDAS, they seem to be new-fangled things that only became apparent in the Internet age. I do remember SOHCAHTOA though.However, the order of operations, where you do powers first, then multiplication, then addition, was an elementary thing taught in the very first algebra class. It was about the second thing taught after the introduction of using letters to represent numbers.

author: thm_w
author_rank: Super Contributor
timestamp: December 20, 2024, 12:34:58 am
content: Quote from: Analog Kid on December 19, 2024, 07:24:30 amhttps://archive.org/details/algebraandtrigon033520mbp/page/n37/mode/2upQuote

author: CatalinaWOW
author_rank: Super Contributor
timestamp: December 20, 2024, 01:14:28 am
content: As the prior example from APL demonstrates there is a big difference between being canonically correct and being clear.Yes, everyone should be familiar with the formal order of operations. But as the huge number of "trick" presentations floating around the internet demonstrates a completely correct expression can be far from clear. It may require some extra characters, maybe even some typesetting, but it is always worth making your intentions clear and correct.

author: Analog Kid
author_rank: Super Contributor
timestamp: December 20, 2024, 01:45:12 am
content: Well then, if one is truly interested in accurately showing a math expression, then one should use parentheses (not "brackets"--brackets are[ ] { }) to make the order of operations perfectly clear, yes?Or you could not do that and just browbeat anyone who misinterprets it.

author: IanB
author_rank: Super Contributor
timestamp: December 20, 2024, 04:20:31 am
content: Quote from: Analog Kid on December 20, 2024, 01:45:12 amOnly when needed. Not always (or often).For example, given a matrix$$A = \begin{bmatrix}a & b \\ c & d\end{bmatrix}$$then the determinant is given by$$|A|=ad-bc$$Everyone universally knows how to read this, and it is not necessary, even ugly, to write:$$|A|=(ad)-(bc)$$

author: IanB
author_rank: Super Contributor
timestamp: December 20, 2024, 04:26:25 am
content: Quote from: CatalinaWOW on December 20, 2024, 01:14:28 amQuote from: Analog Kid on December 20, 2024, 01:45:12 amIn the case of those "trick" questions, then absolutely, yes. But then they wouldn't be trick questions anymore, and the trolling impact would be lost.

author: CatalinaWOW
author_rank: Super Contributor
timestamp: December 20, 2024, 06:09:34 am
content: Quote from: IanB on December 20, 2024, 04:20:31 amI agree. This expression doesn't need parenthesis to be clear.The real message is that thought is required to write a proper (and clear) expression. Reading the expression is not the only opportunity for brainpower. And writing a deliberately unclear expression is the arithmetic equivalent of putting a whoopee cushion on a chair. A juvenile prank that gets old very quickly.

author: tggzzz
author_rank: Super Contributor
timestamp: December 20, 2024, 12:36:54 pm
content: Quote from: CatalinaWOW on December 20, 2024, 01:14:28 amIt is a fundamental mistake, of course, to confuse computer calculations with mathematics.QuoteThe internet is indeed full of "alternative facts" and "opinions of equal value". Sickening, isn't it.

author: tggzzz
author_rank: Super Contributor
timestamp: December 20, 2024, 12:43:19 pm
content: Quote from: Analog Kid on December 20, 2024, 01:45:12 amPresumably you also expect people to make the meaning of every word clear? What a glory that would be. in the sense that Humpty Dumpty used it

author: CatalinaWOW
author_rank: Super Contributor
timestamp: December 20, 2024, 05:12:31 pm
content: Confusing computer calculations with mathematics. I interesting. So in your opinion the exhaustive proofs done in recent years using computers to test the many possibilities are not mathematics?Computer languages are formal definitions (at least when done properly) of a set of operations. As are rules for describing mathematical relations and expressions. In both cases it's is possible to be formally correct, but unclear. It is worth thinking about why they are unclear, even though following the rules precisely. The reasons all come from the fact that our brains aren't computers, not matter how hard we try to force them to be.

author: tggzzz
author_rank: Super Contributor
timestamp: December 20, 2024, 05:52:16 pm
content: Quote from: CatalinaWOW on December 20, 2024, 05:12:31 pmBy "calculations" I was meaning arithmetic calculations. I don't class "if X then Y else Z" (or any glorified variant) as being a calculation.I'll leave professional mathematicians to answer the latter. Question: if nobody can understand such a proof, is the proof valid? That has (does?) worry mathematicians.QuoteWhere they are decently formally defined (i.e. no undefined and implementation defined behaviour), then it is clear that the arithmetic calculation doesnotfollow mathematics definitions.

author: IanB
author_rank: Super Contributor
timestamp: December 20, 2024, 07:23:00 pm
content: Sometimes youneedparentheses. Even BODMAS/PEMDAS can't save you. For example:12÷3÷2 = ?In reality nobody would ever write that, and it does become something of a game.

author: Zoli
author_rank: Frequent Contributor
timestamp: December 20, 2024, 07:29:56 pm
content: Quote from: tggzzz on December 19, 2024, 10:50:03 amISO 80000-2 allows the use of the colon( : ) as ratio(a:b=0.375); the symbol ÷ should not be used. IIRC, the Greek, Latin and Arab arithmetic used colon( : ) as division sign, since fractional arithmetic was treated differently. Maybe the extended use of the fractional sign( /) should be considered bizarre and unnecessary substitution?

author: tggzzz
author_rank: Super Contributor
timestamp: December 20, 2024, 07:48:17 pm
content: Quote from: Zoli on December 20, 2024, 07:29:56 pmI wasn't aware of ISO80000-2, any more than most people are aware of ISO8601 for date formats (emphatically plural!) nor RFC5322 for email address specifications (not so many plurals)I was taught ":" for ratio, and wouldn't use "/" for that.Using "/" for a fraction is common, mainly due to limitations in earlier typing/printing technology.Was ":" used to mean division before and/or after Robert Recorde invented the "=" equals sign in 1557 ?

author: TimFox
author_rank: Super Contributor
timestamp: December 20, 2024, 09:48:59 pm
content: There is also the double ratio, or proportion as inx:y::s:tThe equals sign "=" was promoted since "no two things can be more equal", or"And to auoide the tediouſe repetition of theſe woordes : is equalle to : I will ſette as I doe often in woorke vſe, a paire of paralleles, or Gemowe lines of one lengthe, thus: =, bicauſe noe .2. thynges, can be moare equalle."

author: Zoli
author_rank: Frequent Contributor
timestamp: December 21, 2024, 02:24:21 am
content: Quote from: tggzzz on December 20, 2024, 07:48:17 pmI've seen in physics textbooks(French, German and other languages) dated from the first half of the 20th century, about 45 to 50 years ago.

author: SiliconWizard
author_rank: Super Contributor
timestamp: December 21, 2024, 02:45:03 am
content: Quote from: Zoli on December 21, 2024, 02:24:21 amYes. The division symbol ÷ was more commonly used though. But I'm guessing the simple colon : was used instead when the division symbol was not available as a character. So, basically a simplification of it.

author: IanB
author_rank: Super Contributor
timestamp: December 21, 2024, 04:36:11 am
content: Ratio and division are not the same. For example, 2:3 as a fraction is 2/5 or 2÷5.

author: eugenenine
author_rank: Frequent Contributor
timestamp: December 31, 2024, 02:05:57 am
content: Only one I ever use is droid48 and x48 on my laptop and pc. I use a rom dump from my own 48sx.

author: tooki
author_rank: Super Contributor
timestamp: December 31, 2024, 10:24:10 am
content: Quote from: Analog Kid on December 20, 2024, 01:45:12 amUS English:() = parentheses[] = brackets{} = braces or curly bracketsUK English:() = brackets[] = square brackets{} = curly brackets or bracesI don’t know which usage is common in other English speaking countries.