Order of operations, and where calculators disagree
Most disputes about a calculator's answer come down to precedence rather than arithmetic. Multiplication and division bind more tightly than addition and subtraction, and operators of equal precedence evaluate left to right — so 10 − 3 − 2 is 5, not 9.
The genuinely ambiguous case is implicit multiplication. Expressions of the form 6 ÷ 2(1+2) circulate periodically as viral arguments, and the honest answer is that there is no universal convention: some calculators treat juxtaposition as binding tighter than division and return 1, others treat it as ordinary multiplication and return 9. Both are internally consistent. The lesson is not that one camp is wrong but that the expression is badly written — parentheses cost nothing and remove the ambiguity entirely.
Percentage keys are the other inconsistency. On many calculators 200 + 10% yields 220, because the percent key is interpreted relative to the preceding term, while on others it yields 200.1. Check what your tool does with a case you can verify mentally before trusting it on one you cannot.
Floating point, briefly
Calculations here use IEEE 754 double precision, which stores numbers in binary. Most decimal fractions have no exact binary representation, so 0.1 + 0.2 produces 0.30000000000000004 rather than 0.3 — not a fault, but a consequence of the format, and the same behaviour you will find in essentially every programming language and spreadsheet.
Displayed results are rounded to hide this, which is the right default but means the stored value can differ slightly from what you see. It matters when a result feeds into another calculation: rounding at each step and then multiplying compounds the error, whereas keeping full precision throughout and rounding once at the end does not.
Integers are exact up to 2⁵³, about 9.007 × 10¹⁵. Beyond that, consecutive integers are no longer all representable, so very large values silently round. For money, this is why financial systems generally store amounts as integer minor units — pence or cents — rather than as decimal fractions.
Rounding rules that change the answer
There is more than one correct way to round, and the choice has real consequences. Round-half-up, the method taught in schools, always sends .5 upward, which introduces a small systematic upward bias across many values. Round-half-to-even — banker's rounding — sends .5 to the nearest even digit, so 2.5 becomes 2 and 3.5 becomes 4, and the bias cancels over a large set.
That is why banker's rounding is the default in many financial and statistical systems, and it is the IEEE 754 default too. If you compare a total computed in one system against the same total in another and find a discrepancy of a few pence across thousands of rows, differing rounding modes are a likely explanation.
For money specifically, round once at the end rather than at each intermediate step, and be explicit about the method where it matters. Percentages compound the issue: three values rounded individually to whole percentages frequently sum to 99 or 101 rather than 100, which is expected rather than a mistake.