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=={{anchor|RPN}}Reverse Polish notation==
{{main|Reverse Polish notation|Reverse Polish Lisp}}▼
[[File:Screenshot from 2015-09-10 21-56-23.png|thumb|right|Screenshot of an RPN Calculator program on [[Linux]]]]
[[File:HP-10C programmable calculator.jpg|left|thumb|The [[Hewlett-Packard Voyager series]] of calculators all use RPN input. The "Enter" key is used here to push the value on the display onto the stack.]]
▲{{main|Reverse Polish notation|Reverse Polish Lisp}}
In '''reverse Polish notation''',<ref name="Ball_1978"/> also known as '''postfix notation,''' all operations are entered after the [[operand]]s on which the operation is performed. Reverse Polish notation is parenthesis-free, which usually leads to fewer button presses needed to perform an operation. By the use of a [[Stack (data structure)|stack]], one can enter formulas without the need to rearrange operands.
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=={{anchor|10-Key}}Ten key notation==
[[File:Sharp EL-1192D Calculator.jpg|thumb|This printing calculator made by Sharp uses ten-key notation. Notice the size and placement of the keys, including the extra-large "+/=" and the red "-/=" keys.]]▼
{{see|Keypad}}
▲[[File:Sharp EL-1192D Calculator.jpg|thumb|This printing calculator made by Sharp uses ten-key notation. Notice the size and placement of the keys, including the extra-large "+/=" and the red "-/=" keys.]]
The '''ten-key notation''' input method first became popular with accountants' [[adding machine|paper tape adding machines]]. It generally makes the assumption that entered numbers are being summed, although other operations are supported. Each number entered is followed by its sign (+/−), and a running total is kept. An assumption is made that the last operand can be implicitly used next, so by just entering another + (for example), one will reuse the most recent operand. Ten key input mode is available in printing calculators from companies such as [[Sharp Corporation|Sharp]],<ref>{{cite web |url=http://siica.sharpusa.net/Business-Products/Calculators |title=SIICA.sharpusa.com > Resources > More Products > Calculators |website=siica.sharpusa.net}}</ref> and in software calculators like Judy's TenKey<ref>{{cite web |url=https://www.judysapps.com/TenKey.htm |title=Award-Winning Judy's TenKey Accounting Calculator for Windows |website=www.judysapps.com}}</ref> used by accounting firms. Online tenkey training and certification tools are available as well,<ref>{{cite web |url=https://www.learn2type.com/typingtest/tenkeycertificate.cfm |title=Ten Key Certificate on Learn2Type.com! |website=Learn2Type.com}}</ref><ref>{{cite web |url=http://www.abbyinc.com/abbyinc/KeyPro.asp |title=None |access-date=16 June 2023}}</ref> and some businesses use [[words per minute#Numeric entry|ten key typing speed]] as an employment criterion.
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=={{anchor|Textbook}}Mathematical display==
{{See also|Prettyprint}}
[[File:CalculatorFractions-5550x.jpg|thumb|200x200px|A Casio ''Natural Display'' scientific calculator displaying mixed fractions and their decimal equivalents in pretty-printing]]
[[File:Mathematica dinis surface.png|left|thumb|Pretty-printed commands used to plot [[Dini's surface]] in Mathematica]]
Modern computer algebra systems, as well as many scientific and graphing calculators, allow for "'''pretty-printing'''", that is, entry of equations such that [[Fraction (mathematics)|fractions]], [[Nth root#Definition and notation|surds]] and [[integral]]s, etc. are displayed in the way they would normally be written. Such calculators are generally similar in appearance to those using infix notation, but feature a full dot-matrix display and templates for entering expressions, which are navigated using arrow keys on the calculator. The templates contain spaces for values or expressions to be entered, and empty values would typically result in a syntax error, making it more cumbersome to navigate than standard infix notation; standard infix notation is often an option on such calculators as well.
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* {{cite web |title="Order of operations" and other oddities in school mathematics |author-first=Hung-Hsi |author-last=Wu |author-link=:d:Q102116088 |___location=Berkeley, California, USA |publisher=Department of Mathematics, University of California |date=2007-09-13 |orig-date=2004-06-01 |url=https://math.berkeley.edu/~wu/order5.pdf |access-date=2007-07-03
|url-status=live |archive-url=https://web.archive.org/web/20230918204521/https://math.berkeley.edu/~wu/order5.pdf |archive-date=2023-09-18}} (11 pages)
* {{cite book |title=Order of Operations and RPN |author-first=Greg |author-last=Vanderbeek |date=July 2007 |type=Expository paper |series=Master of Arts in Teaching (MAT) Exam Expository Papers |id=Paper 46 |publisher=[[University of Nebraska Press]] |___location=[[Lincoln, Nebraska]], USA |url=https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1045&context=mathmidexppap |access-date=2020-06-14 |url-status=live |archive-url=https://web.archive.org/web/20200614191608/https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1045&context=mathmidexppap |archive-date=2020-06-14}} (1+2+17 pages)
* {{cite book |title=Keller, Stack und automatisches Gedächtnis – eine Struktur mit Potenzial |language=de |trans-title=Cellar, stack and automatic memory - a structure with potential |editor-first1=Michael |editor-last1=Fothe |editor-first2=Thomas |editor-last2=Wilke |type=Tagungsband zum Kolloquium 14. November 2014 in Jena |___location=Jena, Germany |volume=T-7 |series=GI Series: Lecture Notes in Informatics (LNI) – Thematics |publisher=[[Gesellschaft für Informatik]] (GI) / Köllen Druck + Verlag GmbH |isbn=978-3-88579-426-4 |issn=1614-3213 |date=2015 |orig-date=2014-11-14 |publication-place=Bonn, Germany |url=https://dl.gi.de/bitstream/handle/20.500.12116/4381/lni-t-7.pdf?sequence=1&isAllowed=y |access-date=2020-04-12 |url-status=live |archive-url=https://web.archive.org/web/20200412122706/https://dl.gi.de/bitstream/handle/20.500.12116/4381/lni-t-7.pdf?sequence=1&isAllowed=y |archive-date=2020-04-12}} [https://web.archive.org/web/20221210100112/https://dl.gi.de/handle/20.500.12116/4374/browse?type=title&sort_by=4] (77 pages)
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