Order of Operations - Calculators

Calculators

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 evaluates only 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 =

An expression like 1/2x is interpreted as 1/(2x) 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 rule that multiplication and division are of equal precedence, so 1/2x is read one divided by two and the answer multiplied by x.

When the user is unsure how a calculator will interpret an expression, it is a good idea to use parentheses so there is no ambiguity.