Using percent key on calculator

My calculator has a percent key. I thought that using it to add sales tax to a number would yield the correct total but it gives me a higher amount than it should be. For example if I key in 100+8.25% (using the percent key), the answer should be 108.25, but instead the total appears as 108.99. Why am I getting this incorrect total?

Have you tried other amounts? Are they correct? Or are they off by 74 cents as well? As far as I can tell, you’re using it correctly. Perhaps, it doesn’t like the decimal point? Have you tried 100+825%? That should be calculated as .0825 unless I miss my guess.

On my calculator if I key in 100+8.25% I get 108.25. If I key in 50+6% I get 53. (Actually I never realized you could do this at all with addition.) So are you sure you are keying it in that way? I cannot figure out any method of interpreting that which could yield 108.99.

[1]
[0]
[0]
[Enter]
[8]
[.]
[2]
[5]
[%]
[+]

@Inner Stockler
8.25%=.0825
825% would equal 8.25
Keying in 100+825% yields -13.79 for some reason???
All amounts are proportionately off. If I calculate for 50 instead of 100, the total is off by .37, i.e., I get 54.50 instead of 54.13.
I’m confused.

I’ve arrived at a diagnosis.

Someone spilled soda on your calculator.

@CookingWithGas
Yes, I’m sure I’m entering it correctly. If I key in 50+6%, I get 53.19 instead of 53. There must be some strange setting that I don’t know about. It’s a fairly ancient Casio calculator (model HR-8TE) and I have not been able to locate a user manual for it on line to explain all the possible settings.

I have found different calculators seem to treat the percent key in different ways, so I found it easier to change the percent to a decimal and work that way. Even if I was working with fractions the calculator would accept a decimal in the calculation with no problem.

I don’t know what the problem is, but I do know what my next step would be in trying to figure it out. Somewhere in between 8.25% and 825%, it’s transitioning from an increase to a decrease. I’d try to figure out where that transition is.

It sounds like an odd way to implement a percent function, but I’ll point out that (100% - 8.25%) of 108.99 is almost exactly 100. It is as if instead of multiplying by 1.0825, it is dividing by 0.9175. Same goes for your other example: 50*1.06 = 53, while 50/0.94=53.19.

I think I may have figured out how the calculator is calculating it:

The calculator seems to be basing the percentage on the result, rather than the initial value.

For example:

Working backwards:

Take 825% of -13.79: -113.7675

Now subtract that from -13.79: 99.9775

Close enough to 100 that it makes me think the difference is due to a calculator rounding error.

The other examples in this thread fit this pattern, too.

I have never used the % calc on my calculator so I tried this out of curiosity

100
+
8.25
%
ans

displays on screen as 100+8.25%

and the answer is 1312.121212

What the heck is that

(100+10% gives 1100 if that helps and 100*8.25% gives 8.25)

On my Android calculator app, 100 + 10% = 100.1

WTF. Not exactly intuitive.

Well, the multiplication in spanna’s case is obvious.

8.25% = .0825

.0825 * 100 = 8.25

I have no idea what the hell it’s doing with addition.

It seems to think (on mine) that the % button just means “divide this number by 100 before doing anything else”. Whereas one would expect it to mean “apply this percentage of the preceding number please”.

On RealCalc, on Android, 100 + 10% = 110

But yes, the native Android calculator gives me 100.1. WTF?
However, 100 x 10% = 10, which makes sense.

After more experimentation, I think I know what it’s doing. When you do 100 + 10%, it’s treating the 10% as a fraction, which is 1/10, hence giving you 100.1. That’s mathematically correct, I suppose, but entirely idiotic, because in what circumstances would you want to treat a percentage as a pure fraction? It’s also consistent with the behaviour of the multiplication, since 100 * 0.1 = 10.

100 + 100x10% = 110, which is again mathematically more accurate but so much more convoluted.

100+10% = 100.1 is exactly what I would expect. Maybe it’s my programmer brain, but if I wanted 110% or 1.10 as my answer, I would have entered 100%+10%

ETA: Though I can see a case to be made for a button that’s essentially a macro such that:

100+10(MACRO%) = 100 + (10% * 100)

but I don’t think that button should be the default percent key.

ok I just googled my calculator and got the manual

looks like to add 8.25% I should have keyed the following

100*8.25%+

not exactly intuitive

Not really.

I typically wouldn’t use the % key at all for this calculation. To add 8.25% to 100, I would enter:

100 * 1.0825

I confess I never really understood the results I got with the % key, but this method always got the job done, so…

That works for 100, but what would you do for, say, 8.25% of 67?
I just enter 67+67*.0825, and get the correct results. I never found a calculator that used the percentage key the same way each time, and never bothered to use it when it had one.