How can you tell whether your calculator follows the standard order of operations?
A quick test that I use to find out if a calculator follows the standard order of operations is to enter:
1 + 2 * 3 =If the answer is 7, then the calculator follows the standard order of operations, if the answer is 9 then it doesn’t. If no answer appears, then you are probably standing at IKEA trying to use one of the dummy calculators.
Why it works
A calculator that does not follow the standard order of operations will apply the operators (plus, times, minus, etc.) as they come. In the above example, such a calculator would first add 1 and 2 (which is 3) and then multiply the result by 3 (which is 9).
A calculator that does follow the standard order of operations will first evaluate the “priority” of all operators in a calculation and then calculate the result evaluating the higher-priority operators first. In the above example the [*] operator has a higher priority than the [+] operator. Therefore the calculator evaluates 2 * 3 first (which is 6) and then adds 1 to the result (which is 7).
The standard order of operations
The standard order of operations is a rule which states, that binary operators with a higher priority are evaluated before binary operators with a lower priority. The priorities are as follows:
- Exponents
- Multiplication/Division
- Addition/Subtraction
For more information on the order of operations see this Wikipedia article.
March 13th, 2009 at 6:55 pm
Hello, I am taking Algebra 2 and I have been using this calculator and have always had positive results. However, today I am doing scientific notation and I could not seem to get the right answers although I was following the directions of my Algebra book and also the instructions on this site. It seems that the exponent key might not be working properly, because I found another calculator to use that gave me the right answers. I just wanted to let you know in case the exponent key is not working right. It could be that I wasn’t using it correctly, but then again the other scientific calculator seemed to work. Thank you.
March 13th, 2009 at 7:16 pm
Hello Alison,
thanks for letting me know, that the calculator might not be working properly. I am not aware of a problem with the scientific notation or exponent function, but if you send me an example of an equation, where the calculator fails, I will look into it.
March 13th, 2009 at 11:32 pm
This is one of the problems I was having trouble with:
-17 5
( 0.00042 x 10 )( 568,425 x 10 )
Things seemed to go wrong when I used a negative exponent. Again, I might have been using the calculator incorrectly. Thanks for your help.
March 13th, 2009 at 11:56 pm
sorry. the problem was supposed to be:
-17 5
( 0.00042 x 10 )( 568,425 x 10 )
Sorry for all the trouble I’m causing.
March 13th, 2009 at 11:56 pm
It does not work…
March 14th, 2009 at 3:40 pm
Hello Alison,
I’m supposing you meant ( 0.00042 x 10^-17 )( 568,425 x 10^5 ), where the ^ sign means “to the power of”. If that is correct, then the solution would be 2.387385 x 10^-13, which I get on all the calculators that I have tried, including the one on this site. If I misinterpreted your problem then please let me know. If you use an email program and set the font to “Courier” or “Courier New” it might be easier for you to depict mathematical problems. My email address is marek [at] calculator-tab [dot] com.
April 4th, 2009 at 10:48 am
Thank you.
Well done – [****]^
March 24th, 2010 at 4:34 am
hi, when i did 4.60*27 it took off the zero in 4.60 please fix it!
Thanks,
cmbeke
March 24th, 2010 at 9:03 am
Hello cmbeke,
that the last zero(s) after a decimal point disappear(s), when you continue your calculation is not a mistake – it’s intentional. It to tells you, that those zeros are not needed: 4.60 or 4.600 or 4.6000 are all exactly the same as 4.6.
For a future version of the calculator I am planning a feature which will let you set the number of decimal places under options.