HP RPN Scientific Calculator Buyers Guide (HP50g, 48gII, 40gs & 39gs)
Know How to Use an RPN Calculator
A logic system was developed in the 1920s which allowed mathematical constructions to be defined without parentheses by placing the operators before (prefix notation) or after (postfix notation) the operands. The prefix notation was called Polish Notation. Later in time, Hewlett Packard adjusted the postfix notation for a calculator keyboard, added a stack to hold the operands and functions to reorder the stack. This postfix notation was called Reverse Polish Notation (RPN.)
Do you recall how you first learned to do math? We were taught to write down the numbers we wanted to sum in a column, draw a line and then put the sum below the line. RPN works the same way. Take your calculator and key in 20. Press the ENTER key to tell the calculator that you are done keying this number. Now key in 18 and tell the calculator to add it to the previous number by pressing the + key. The result of 38 will be displayed. Subtraction, multiplication and division all work the same way but with the -, ×, and ÷ keys substituted for the + key.
This also works for more than two numbers. To multiply the numbers 3, 4 and 5 together press 3 ENTER 4 ×5 × and read the result. Note that you didn't press ENTER after the 2nd and 3rd numbers because the operation key makes it clear that you are finished keying these numbers.
Remember that RPN calculators perform mathematical operations immediately when you press the operation keys so the number(s) must be entered first. There are no "pending operations" or precedence in RPN calculators. When multiple numbers must be entered in sequence, separate them with the ENTER key. Many functions require only one number. On an RPN calculator, you still enter the number and then press the operation key and see the result. Many calculators that claim to be algebraic use the same method since it takes less keystrokes than real algebraic syntax. For example, to compute the sine of 20 press 2 0 SIN and read the result. To compute e6 press 6 ex.
The great thing about RPN is that it extends to arbitrarily difficult expressions without parentheses and precedence rules. You can easily evaluate more elaborate expressions than the ones shown above. Just start with the innermost set of parentheses and work outwards as you would to solve the expression with a pencil and paper. For example to evaluate ([(4+5)(2+3)+6]/(8+7))^9 press: 4 ENTER 5 + 2 ENTER 3 + × 6 + 8 ENTER 7 + ÷ 9y^x and read a result of 60716.99. Here is the sequence broken down into steps; 4 ENTER 5 + "Adds 4 and 5 - one of the innermost terms", 2 ENTER 3 + " Adds 2 and 3 another inner term", x "takes 4+5 in the Y register and 2+3 in X so multiply them", 6 + "Adds 6 to the result to complete (4+5)(2+3)+6", 8 ENTER 7 + " Adds 8 and 7 to compute the denominator, ÷ "Divides into the numerator previously calculated", 9 y^x "Raises the previous result to the 9th power."
This is the same order that you would have solved the expression by hand and the calculator will show the result of each sub expression which helps you catch errors. After a little more practice, RPN will become second nature and you may never want to use an algebraic calculator again.
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