Percentage operation gives different results with two scientific calculator The operation is: $21.99 + 9.75$$\%$
On the Texas Instruments model TI36X-Pro the answer is: $22.0875$
But when I tried on the Casio FX-991ES Plus the result is: $24.134025$
Which is the correct answer?
And how these two calculators reach different results?
 A: Since $9.75\% = 0.0975$, the correct answer is $22.0875$.
The number you got with the second calculator is actually $21.99 \cdot 1.0974$, which is the number $21.99$, increased by $9.75$ percent.
With more simple numbers:
If I add $\frac12$, which is $50\% $ to the number $10$, I will get $10+\frac12 = \frac{21}{2}=10.5$. However, if I increase $10$ by $50\%$, I will increase it by $5$ (because $5=\frac12 10$) and get $15$.
A: It depends on how we 'read' $21.99 + 9.75\%$
(1)  As $\%$ is derived from the latin 'per centum' (which means 'out of one hundred'), we have
$$ 9.75\% = \frac{9.75}{100} = 0.00975 $$
giving answer one.
(2) Many calculators allow the input 21.99 + 9.75% being a shortcut for the operation 'add 9.75% of 21.99 to the given 21.99', which is 
$$ 9.75\% \cdot 21.99 = 2.144025 $$
giving the second answer.
If I should choose the 'correct' one, this would be (1), but the better way is not to use notation like that.
A: Other calculators give yet more answers:


*

*Simply divide argument by 100:
${\bf 22.0875} = 21.99 + (9.75 / 100)$
e.g. Texas Instruments TI36X-Pro

*Use argument to add mark up1:
${\bf 24.134025} = 21.99 \times (1 + 9.75 / 100)$
e.g. Casio FX-991ES Plus, MS Windows Calculator  

*Use argument to add margin:
${\bf 24.36565} = 21.99 \div (1 - 9.75 / 100)$
e.g. Casio DS-20

*Total as percent of second argument:
${\bf 325.53846} = (21.99 + 9.75) \div 9.75 \times 100$
e.g. Casio fx-3400P, Casio fx-115W, Casio fx-260

*Some calculators have no percentage button.
e.g. Texas Instruments TI84 Plus
There is no consensus for the calculator keystrokes "21.99+9.75%=", and probably not2 for the notation "$21.99+9.75\%$", so there isn't a right answer.  
And that's just for addition3.  So don't rely on the percent button without knowing what that particular model of calculator does!

1. I have found the mark up behaviour to be the most common for no-frills office calculators.


2. What would "$1.23 + 9.8\% + 3.32 + 66.4\%$" mean?


3. See also Calculators are needlessly bad by Harold Thimbleby (Int. J. Human-Computer Studies (2000) 52, 1031-1069).

A: The Casio one adds $9.75\%$ of $21.99$, which is $2.144025$.
The Texas one adds $9.75\% = 0.0975$ as a plain number.
As to which one is correct, that depends on the specific question.
