Different calculators follow different orders of operations. Most non-scientific calculators without a stack work left to right without any priority given to different operators, for example giving
while more sophisticated calculators will use a more standard priority, for example giving
The Microsoft
Calculator program uses the former in its standard view and the latter in its scientific view.
The non-scientific calculator expects two operands and an operator. When the next operator is pressed, the expression is immediately evaluated and the answer becomes the left hand of the next operator. Advanced calculators allow entry of the whole expression, grouped as necessary, and only evaluates when the user uses the equals sign.
Calculators may associate exponents to the left or to the right depending on the model. For example, the expression a ^ b ^ c on the TI-92 and TI-30XII (both Texas Instruments calculators) associates two different ways:
The TI-92 associates to the right, that is
a ^ b ^ c = a ^ (b ^ c) =
whereas, the TI-30XII associates to the left, that is
a ^ b ^ c = (a ^ b) ^ c = (
ab)
c. An expression like 1/2
x is interpreted as 1/(2
x) by TI-82, but as (1/2)
x by TI-83. While the first interpretation may be expected by some users, only the latter is in agreement with the standard rules stated above.