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Order of operations
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==Calculators== {{main article|Calculator input methods}} Different calculators follow different orders of operations.{{r|BS}} Many simple calculators without a [[stack machine|stack]] implement [[chain input]], working in button-press order without any priority given to different operations, give a different result from that given by more sophisticated calculators. For example, on a simple calculator, typing <code>1 + 2 Γ 3 =</code> yields 9, while a more sophisticated calculator will use a more standard priority, so typing <code>1 + 2 Γ 3 =</code> yields 7. Calculators may associate exponents to the left or to the right. For example, the expression <code>''a''^''b''^''c''</code> is interpreted as ''a''<sup>(''b''<sup>''c''</sup>)</sup> on the [[TI-92]] and the [[TI-30XS MultiView]] in "Mathprint mode", whereas it is interpreted as (''a''<sup>''b''</sup>)<sup>''c''</sup> on the [[TI-30XII]] and the TI-30XS MultiView in "Classic mode". An expression like <code>1/2''x''</code> is interpreted as 1/(2''x'') by [[TI-82]],{{r|Peterson}} as well as many modern [[Casio]] calculators{{r|Casio}} (configurable on some like the [[Casio fx-9750GIII|fx-9750GIII]]), but as (1/2)''x'' by [[TI-83]] and every other TI calculator released since 1996,{{r|TI 2011}}{{r|Peterson}} as well as by all [[Hewlett-Packard]] calculators with algebraic notation. While the first interpretation may be expected by some users due to the nature of [[implied multiplication]],{{r|TI 1982}} the latter is more in line with the rule that multiplication and division are of equal precedence.{{r|Peterson}} When the user is unsure how a calculator will interpret an expression, parentheses can be used to remove the ambiguity.{{r|Peterson}} Order of operations arose due to the adaptation of [[infix notation]] in [[standard mathematical notation]], which can be notationally ambiguous without such conventions, as opposed to [[postfix notation]] or [[prefix notation]], which do not need orders of operations.{{r|Simons}}{{r|KS}} Hence, calculators utilizing [[reverse Polish notation]] (RPN) using a [[stack (data structure)|stack]] to enter expressions in the correct order of precedence do not need parentheses or any possibly model-specific order of execution.{{r|Ball}}{{r|Vanderbeek}}
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