To sum up my question would be is a calculator not following the standard left to right order of operations considered a bad calculator? Is this being a universal convention means that programs or calculators that do not follow it are wrong?
My college uses a self-made program for us to do our homework assignments. I'm having an argument with one of its technical support guys as to whether the program is wrong for not following this convention, since my answer was marked wrong for giving an answer in this format: A / B * C, instead of one with parentheses ( i.e. (A / B) * C ). He claims that the answer is ambiguous and could also be interpreted as A / (B * C). In my opinion since most calculators, programming languages, and the likes do follow a convention then it should too.
In mathematics, $a/b c$ is clearly ambiguous and the ambiguity needs to be removed by writing $\frac{a}{b} c$ or $\frac{a}{bc}$ or $(a/b)c$ etc. In programming languages it is true that most languages such as python, c++, fortran etc give the same precedence to * and /, and a "left associativity" rule, but computer languages have a much wider range of applications than just arithmetic expressions between numbers, so I don't think it can be considered a general rule. Do you know that old pocket Hewlett Packard calculators used reverse polish evaluation, and the same expression was written
A B / C *?My conclusion is that it is always better to remove the ambiguities by yourself.