HP 35s User Manual

							 
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HP 35s  Using Register Arithmetic 
 
hp calculators - 3 - HP 35s  Using Register Arithmetic - Version 1.0 
 When ! is pressed, the symbol “A..Z” appears at the top of the screen. This tells the user that the 
next key pressed should be one of the keys with letters A to Z at their lower right, and that the 
corresponding letter will be used. For the letter “M”, press the , key. The number is stored in M, but 
remains on the lower line of the screen, as shown in Figure 1 (which shows the display in algebraic mode). 
  
 Figure 1 
  
  Store the Moon’s mass in register T as well, so that the Earth’s mass can be added to it. The mass has 
already been stored in M but it is still available to be stored in T as well. Figure 2 shows the screen in 
algebraic mode. 
  
 !- (Note: In algebraic mode, press + after the -) 
 
 Figure 2 
  
 Now type the mass of the Earth and store it in register E. To use register E, press . when the A..Z 
symbol is at the top of the screen. This is not the same as the key labeled # used for entering powers of 
10. 
  
 /$&(0#%)!1 
  
 The mass of the Earth is now in register E and is still on the lower line of the screen. To add it to the mass 
of the Moon already in register T, use the STO+ command in RPN mode only. 
  
 !2- 
  
 In RPN mode, this takes the number in the lower line of the display and adds it to register T. The number is 
still available for further use. It is still the “current number”, i.e., the number is still in stack register X. Figure 
3 assumes RPN mode. 
  
 Figure 3 
 
 In algebraic mode, it is necessary to key the following to perform a STO+ equivalent. NOTE: The resulting 
value displayed is different in algebraic mode when compared to RPN mode. Figure 4 assumes algebraic 
mode. 
 
 23-!- 
 
 Figure 4   
						

							 
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HP 35s  Using Register Arithmetic 
 
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Answer: The mass of the Moon is now in register M, the mass of the Earth is in register E, and the mass of the 
Earth-Moon twin system is in register T. The mass of the Earth is also still in the current register, as shown 
in Figure 2. To confirm that the number in register T is the sum of the two masses, view register T by 
pressing: 
  
 45- 
  
 Figure 5 
 
In RPN mode, the STO+ command adds the current number to the register selected by its name, STO- subtracts the 
current number from the named register, STO! multiplies the named register by the current number and STO divides 
the named register by the current number. In all these cases in RPN mode, the number itself is unchanged and 
continues to be the current number. As it has not changed, the value in the LastX register also remains unchanged. 
 
Practice Example: Calculating Using RCL Arithmetic in RPN mode 
 
Example 2: If the Earth-Moon system is called a twin system, the mass of the Moon should be fairly similar to the mass 
of the Earth. How do they compare? 
 
Solution: The mass of the Earth is still in the current register. Recall the mass of the Moon from register M and divide 
it into the current register. Press these keys. 
  
 36* 
  
 The result of the division is now in the current register. 
  
 Figure 6 
 
Answer: The ratio of the masses of the Earth and the Moon is about 1:81. The Moon’s mass is only about 1.2% that 
of the Earth’s, not really a twin. Nevertheless, the two are much closer in mass than any other major planet-
satellite system. For example the mass of Ganymede is 0.0078% of the mass of Jupiter, and the mass of 
Deimos is 0.0000017% of the mass of Mars. Only Charon and Pluto are closer, with Charon having about 
15% of the mass of Pluto – and not all planetary scientists are willing to consider Pluto to be a planet. 
 
In RPN mode, when 3 is pressed, followed by an arithmetic operation and a letter, then the number in the chosen 
register is recalled and added to, subtracted from, multiplied by, or divided into, the current register. As opposed to STO 
arithmetic, RCL arithmetic changes the current number and leaves the stored number unchanged. Because the current 
number is changed, its previous value is stored in the LastX register for re-use in RPN mode. 
 
Storage Arithmetic in a Program 
 
As these examples show, STO and RCL arithmetic make some calculations easier to carry out. It is generally quicker to 
use a STO or RCL arithmetic operation rather than to RCL a number, calculate with it, and then STO the result. Quite   
						

							 
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HP 35s  Using Register Arithmetic 
 
hp calculators - 5 - HP 35s  Using Register Arithmetic - Version 1.0 
apart from this, many users find that storage register arithmetic has important applications in programs. There are three 
reasons for this. 
  
(1) Each STO or RCL instruction takes one less step in a program than STO or RCL followed by a separate 
arithmetic command. Saving a step in a program makes it shorter, faster and easier to read. 
   
(2) STO arithmetic does not use the RPN stack and does not change the LastX register. This means that 
programs can be written to work in the same way as built-in HP 35s functions, to replace the original 
number with a calculated result, keep a copy of the original number in LastX, and leave the rest of the stack 
unchanged. Such programs can then be used like built-in functions, and can be called from other 
programs. 
  
This training aid has shown how STO and RCL arithmetic can be useful in keyboard calculations and in programming. 
With experience, users can find many occasions where storage arithmetic on the HP 35s is a real help in their work. 
   
						

							 
 
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HP 35s  Using the built-in constants 
 
 
 
 
 
 
 
The built-in constants 
 
Practice using the built-in constants 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
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HP 35S  Using the built-in constants 
 
hp calculators - 2 - HP 35S  Using the built-in constants - Version 1.0 
The built-in constants 
 
The HP 35s includes 41 physics constants built into the ! menu. These constants remove the need to keep a 
table of frequently used constants handy or to look them up in a reference manual. These constants can be used when 
doing calculations in run mode, within a program, or within an equation. The 41 constants included are: 
 
Speed of light in vacuum 
Standard acceleration of gravity 
Newtonian constant of gravitation 
Molar volume of ideal gas 
Avogadro constant 
Rydberg constant 
Elementary charge 
Electron mass 
Proton mass 
Neutron mass 
Muon mass 
Boltzmann constant 
Planck constant 
Planck constant over 2 pi 
Magnetic flux quantum 
Bohr radius 
Electric constant 
Molar gas constant 
Faraday constant 
Atomic mass constant 
Magnetic constant 
Bohr magneton 
Nuclear magneton 
Proton magnetic moment 
Electron magnetic moment 
Neutron magnetic moment 
Muon magnetic moment 
Classical electron radius 
Characteristic impendence of vacuum 
Compton wavelength 
Neutron Compton wavelength 
Proton Compton wavelength 
Fine structure constant 
Stefan–Boltzmann constant 
Celsius temperature 
Standard atmosphere 
Proton gyromagnetic ratio 
First radiation constant 
Second radiation constant 
Conductance quantum 
The base number e of natural logarithm 
 
In algebraic mode, the constants are shown as the corresponding symbol. In RPN mode, when doing calculations 
manually, the constants are shown as their numeric values. In either mode, the constants are shown as their 
corresponding symbol when in equation mode or within a program. 
 
The HP 35s displays between 4 to 6 constants on the screen, depending on which “page” of the constant menu is being 
viewed. The first two pages are shown in example 1 below. To move from one page to the next, you can press # to 
move down a page or $ to move up a page. To move across a page, press % to move right and & to move left. 
Once you are on the page, you can select a constant by pressing the numeric key indicating its position on the page, 
with 1 selecting the first constant shown, 2 the second, etc. 
 
Practice using the built-in constants 
 
Example 1: What is the ratio of a proton’s mass to an electron’s mass? 
 
Solution: These constants are on the second displayed page of constants. The first page looks like this: 
 
 Figure 1 
   
						

							 
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HP 35S  Using the built-in constants 
 
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 The second page looks like this. To move from one page to the next, you can press # to move down a 
page or $ to move up a page. 
 
 Figure 2 
  
 In RPN mode, press: !#%%!#% 
 
 Figure 3 
 
 The display is now showing the two mass values. Press ( to compute the ratio. 
 
 Figure 4 
 
 In algebraic mode, press: !#%%(!#% 
 
 Figure 5 
 
Answer:  The proton is approximately 1836 times more massive than an electron. 
 
Example 2: A space probe is traveling at 50,000 miles per hour. How many times faster would it have to travel to reach 
10% of the speed of light? 
 
Solution: In RPN mode, press: 
 
 !)*(+
 
 Now convert the space probe’s speed to miles per second. 
 
 ,****-*(-*( 
 
 Now compute the number of times faster the probe would have to travel to reach 10% of the speed of light 
by dividing the two values. 
 
 ( 
 
 In algebraic mode, press: 
 
 4!()*%(+
   
						

							 
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HP 35S  Using the built-in constants 
 
hp calculators - 4 - HP 35S  Using the built-in constants - Version 1.0 
e space probe’s speed to miles per second. 
4,****(-*(-* 
  the number of times faster the probe would have to travel to reach 10% of the speed of light 
by pressing: 
  
 Now convert th
  
 
 
Now compute
 
 Figure 6 
Answer
 
:  er than its present speed to reach 10% of 
the speed of light. Figure 6 shows the result in algebraic mode. 
 
The space probe would have to travel over two million times fast
   
						

							 
 
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HP 35s  Averages and standard deviations 
 
 
 
 
Averages and standard deviations 
 
Practice solving problems involving averages and  
standard deviations 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
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HP 35s  Averages and standard deviations 
 
hp calculators - 2 - HP 35s  Averages and standard deviations - Version 1.0 
Averages and standard deviations 
 
The average is defined as the sum of all data points divided by the number of data points included. It is a measure of 
central tendency and is the most commonly used. A standard deviation is a measure of dispersion around a central 
value. To compute the standard deviation, the sum of the squared differences between each individual data point and 
the average of all the data points is taken and then divided by the number of data points included (or, in the case of 
sample data, the number of data points included minus one). The square root of this value is then taken to obtain the 
standard deviation. The property of the standard deviation is such that when the underlying data is normally distributed, 
approximately 68% of all values will lie within one standard deviation on either side of the mean and approximately 95% 
of all values will lie within two standard deviations on either side of the mean. This has application to many fields, 
particularly when trying to decide if an observed value is unusual by being significantly different from the mean. 
 
On the HP 35s, values are entered into the statistical / summation registers by keying in the number (or pair of numbers) 
desired and pressing !. This process is repeated for all numbers or pair of numbers.  When entering a pair  
of numbers in RPN or algebraic mode, key the Y value, press , then key the X value and press !. 
 
To view the mean, press #$. To view the standard deviation, press %&. When either of these is pressed, the 
HP 35s displays a menu of possible values. Items on this menu are viewed by pressing the  or ( parts of the 
cursor keys at the top of the HP 35s. 
 
To use a value displayed on the menu, press the  button and the value will be copied for further use. This is 
illustrated in the problems below.  
Practice solving problems involving averages and standard deviations  
Example 1: The sales price of the last 10 homes sold in the Parkdale community were: $198,000; $185,000;  
 $205,200;$225,300; $206,700; $201,850; $200,000; $189,000; $192,100; $200,400. What is the 
 average of these sales prices and what is the sample standard deviation? Would a sales price of  
 $240,000 be considered unusual in the same community?  
Solution: Be sure to clear the statistics / summation memories before starting the problem.  
 %)*+
+
 The keystrokes are the same whether in RPN or algebraic mode: 
 
 ,-.///!,.0///!1/01//!+
+1102//!1/34//!1/,.0/!+
+1/////!,.-///!,-1,//!+
+1//*//! 
  
 To find the average, press: #$. Figure 1 displays the menu shown. 
 
 Figure 1 
 
 To find the sample standard deviation, press: %&. Figure 2 displays the menu shown. +