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HP 35s User Manual

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    hp calculators 
     
     
     
     
    HP 35s  Unit Conversions 
     
     
     
     
     
    Metric units and Imperial units 
     
    Conversion keys 
     
    Practice working problems involving conversions 
     
    Performing conversions that are not built in 
     
    Special considerations for temperature conversions 
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
     
       
    						
    							 
    hp calculators 
     
    HP 35s  Unit Conversions 
     
    hp calculators - 2 - HP 35s  Unit Conversions - Version 1.0 
    Metric units and Imperial units 
     
    Measurements of quantities such as length, mass or temperature use units. Metric units include centimeters and meters, 
    grams and kilograms, or Celsius and Kelvin degrees. Imperial units include feet and yards, ounces and pounds, or 
    Fahrenheit and Rankine degrees. The HP 35s provides eight functions for converting to and from Metric units. These 
    conversions are useful for many problems in engineering, mathematics, and physical and biological sciences. They can 
    also be used to create additional conversions, through HP 35s equations and programs.  
     
    Two training aids describe unit conversions on the HP 35s. This aid describes mass, length and volume conversions. 
    Temperature conversions are more complicated; a simple example is given in this training aid and a second training aid 
    describes conversion of temperature units in detail. For coordinate, angle and time conversions see the separate training 
    aids, for example angle conversions are covered in the training aid on angle conversions and angle arithmetic. 
     
    Conversion keys 
     
    The unit conversion functions are on the right and left shifted !#$% and & keys. The available 
    conversions are as follows: 
     
    ( for pounds to kilograms 
    )*for kilograms to pounds 
    < for miles to kilometers 
    ); for kilometers to miles 
    + for Fahrenheit to Centigrade 
    ), for Centigrade to Fahrenheit 
    - for inches to centimeters 
    ). for centimeters to inches 
    / for gallons to liters, and 
    )0 for liters to gallons. 
     
    The right and left shifted functions on each key are the inverse of each other. Ways to build up other conversions from 
    them are shown below. 
     
    Note that conversions to Metric units are always on the right-shifted leys, and conversions from Metric units are on the 
    corresponding left-shifted keys. 
     
    Conversions of lb/kg, of in/cm, mile/km and of gal/l involve only multiplication by a conversion factor. Conversions of 
    °F/°C require addition or subtraction of an offset constant as well as multiplication; they are described in more detail in 
    the separate training aid on temperature conversions. 
     
    Practice working problems involving conversions 
     
    Example 1: Convert 10 inches to centimeters 
     
    Solution: In RPN mode, type the number 10 and then press the right-shifted $key. 
     
     12-
       
    						
    							 
    hp calculators 
     
    HP 35s  Unit Conversions 
     
    hp calculators - 3 - HP 35s  Unit Conversions - Version 1.0 
     In algebraic mode, do the same. Pressing 3 completes the calculation, but this is not necessary 
    unless the conversion is part of a longer calculation. 
     
     -123
     
     Figure 1  
    Answer: 25.4 centimeters.  
     
    Example 2: How many gallons is 25 liters? 
     
    Solution: In RPN mode, type the number 25 and then press the left-shifted !key. 
     
     !$)0
     
     In algebraic mode, do the same. Again, pressing 3 completes the calculation, but is not necessary 
    unless the conversion is part of a longer calculation. 
     
     )0!$3 
     
     Figure 2 
     
    Answer: 6.6043 gallons.  
     
    Example 3: Convert 16 square inches to square centimeters 
     
    Solution: A square inch is an inch times an inch. After one - conversion, the units become centimeters 
    times inches. After a second - conversion, the units become centimeters times centimeters, or 
    square centimeters. So, in this case, conversion to centimeters is carried out twice, to give square 
    centimeters. 
     
     In RPN mode, type the number 16 and then press the right-shifted %key twice. 
     
     1%--
     
     In algebraic mode, do the same. Again, pressing 3 completes the calculation, but is not necessary 
    unless the conversion is part of a longer calculation.  
     --1%3 
     
     Figure 3 
       
    						
    							 
    hp calculators 
     
    HP 35s  Unit Conversions 
     
    hp calculators - 4 - HP 35s  Unit Conversions - Version 1.0 
     Another way to do this is to take the square root of 16 cm², giving 4 cm, then convert this to inches, then 
    take the square. Figure 4 shows the result and confirms that the method used above is correct.  
     4-51%3 
     
     Figure 4 
     
    Answer: 103.2256 square centimeters.  
     
    Example 4: Convert 5 yards to meters 
     
    Solution: The conversion keys use inches and centimeters, so it is necessary to go from yards to inches, then 
    convert inches to centimeters, and finally go from centimeters to meters.  
     In RPN mode, type the number 5, multiply by 3 to go to feet, and multiply by 12 to go to inches. Now press 
    the right-shifted %key to convert inches to centimeters. Finally divide by 100 to convert centimeters to 
    meters.  
     $3671!7-1228 
     In algebraic mode, the order is different, and 3 must be used at the end to complete the whole 
    calculation 
     
     -$7671!981223
     
     Figure 5  
    Answer: 4.572 meters.   
    Performing conversions that are not built in  
    Example 5: As the density of water is 1 gm/cm³, what is it in lb/ft³ ?   
    Solution: This conversion is not built into the calculator. As in examples 3 and 4, it is therefore necessary to separate 
    the calculation into the basic units, and then convert each unit. In this example, the steps required are:  
    ! Convert gm to kg, by dividing by 1,000 
    ! Convert kg to lb with )* 
    ! Convert 1/cm to 1/in three times, as the cm are cubed. A short cut for converting inverse units is to 
    notice that this is the same as doing the opposite transformation. So, converting 1/cm to 1/in can be 
    done with -. 
    ! Convert 1/in³ to 1/ft³ by multiplying by 12 cubed.  
     In RPN mode, the above should be done with these keys:  
     1312228)*---1!36:7   
    						
    							 
    hp calculators 
     
    HP 35s  Unit Conversions 
     
    hp calculators - 5 - HP 35s  Unit Conversions - Version 1.0 
     In algebraic mode, the following keys are used instead; note that 3 is needed to complete the 
    calculation.  
     ---)*181222971!:63
    
     Figure 6  
    Answer: The density of water is close to 62.4 pounds per cubic foot. 
     
    Special considerations for temperature conversions 
     
    Special care must be taken with temperature conversions. The two commands + and ), convert 
    temperatures but not temperature differences. The following example shows a simple temperature conversion, for more 
    details see the separate training aid on temperature conversions. 
     
    Example 8: What is 20 degrees Celsius in Fahrenheit? 
     
    Solution: In RPN mode, type the number 20 and then press the left-shifted &key. 
     
     !2),
     
     In algebraic mode, do the same. As usual, pressing 3 completes the calculation, but is not necessary 
    unless the conversion is part of a longer calculation. 
     
     ),!23 
     
     Figure 7 
     
    Answer: 68 degrees Fahrenheit.  
       
    						
    							 
     
    hp calculators 
     
     
     
     
    HP 35s  Temperature Conversions 
     
     
     
     
    Metric units and Imperial units 
     
    Conversion keys 
     
    Practice working problems involving  
    temperature conversions 
     
    Conversion of temperatures and  
    conversion of temperature differences 
     
    Other temperature scales 
     
    Using equations and programs for  
    complicated conversions 
     
     
     
     
     
     
     
     
     
     
     
     
     
     
       
    						
    							 
    hp calculators 
     
    HP 35s  Temperature Conversions 
     
    hp calculators - 2 - HP 35s  Temperature Conversions - Version 1.0 
    Metric units and Imperial units 
     
    Measurements of quantities such as length, mass or temperature use units. Metric units include centimeters and meters, 
    grams and kilograms, or Celsius and Kelvin degrees. Imperial units include feet and yards, ounces and pounds, or 
    Fahrenheit and Rankine degrees. The HP 35s provides ten functions for converting to and from Metric units. These 
    conversions are useful for many problems in engineering, mathematics, and physical and biological sciences. They can 
    also be used to create additional conversions, through HP 35s equations and programs.  
     
    Two training aids describe unit conversions on the HP 35s. A separate training aid describes mass, length and volume 
    conversions. Temperature conversions are more complicated; this training aid covers temperature units in detail. For 
    coordinate, angle and time conversions see the separate training aid on angle conversions and angle arithmetic. 
     
    Conversion keys 
     
    The unit conversion functions are on the right and left shifted !#$% and & keys. The available 
    conversions are as follows: 
     
    ( for pounds to kilograms 
    )*for kilograms to pounds 
    < for miles to kilometers 
    ); for kilometers to miles 
    + for Fahrenheit to Centigrade 
    ), for Centigrade to Fahrenheit 
    - for inches to centimeters 
    ). for centimeters to inches 
    / for gallons to liters, and 
    )0 for liters to gallons. 
     
    The right and left shifted functions on each key are the inverse of each other. Ways to build up other conversions from 
    them are shown below. 
     
    Note that conversions to Metric units are always on the right-shifted leys, and conversions from Metric units are on the 
    corresponding left-shifted keys. 
     
    Conversions of lb/kg, of in/cm, mile/km and of gal/l involve only multiplication by a conversion factor. Conversions of 
    °F/°C require addition or subtraction of offset constants as well as multiplication, and are therefore described in this 
    training aid, in more detail. 
     
    Practice working problems involving temperature conversions 
     
    Special care must be taken with temperature conversions. The two commands + and ), convert 
    temperatures, as the first two examples below show, but they do not convert temperature differences. 
     
    Example 1: Many photographic film developers are designed to work best at 20 degrees Celsius. What is 20 degrees 
    Celsius in Fahrenheit? 
     
    Solution: In RPN mode, type the number 20 and then press the left-shifted &key. 
       
    						
    							 
    hp calculators 
     
    HP 35s  Temperature Conversions 
     
    hp calculators - 3 - HP 35s  Temperature Conversions - Version 1.0 
     !1), 
    
     In Algebraic mode, do the same. Pressing 2 completes the calculation, but is not necessary unless 
    the conversion comes at the end of a longer calculation. 
     
     ),!12 
     
     Figure 1 
     
    Answer: 20 degrees Celsius is 68 degrees Fahrenheit.  
     
    Example 2: What is –40 degrees Fahrenheit when measured in degrees Celsius? 
     
    Solution: In RPN mode, type the number 40, change the sign, and then press the right-shifted &key. 
     
     #13+
     
     In Algebraic mode, do the same. Again, pressing 2 completes the calculation, but is not necessary 
    unless the conversion is part of a longer calculation. 
     
     +#132 
     
     Figure 2 
     
    Answer: The result is –40. That is not an error – this example shows that at –40 degrees the Celsius and Fahrenheit 
    scales coincide. 
     
    Conversion of temperatures and conversion of temperature differences 
     
    With most measurements, zero is an absolute minimum. A length of zero inches or zero centimeters is the smallest 
    possible length, and zero is zero in either of these units. Temperatures are different. Zero degrees Celsius is the freezing 
    point of water at Standard Pressure, but the lowest possible temperature is Absolute Zero, –273.15 degrees Celsius. In 
    degrees Fahrenheit, the freezing point of water is 32 degrees, and Absolute Zero is –459.67 degrees Fahrenheit. 
     
    This means that a conversion from a measurement of 20°C to Fahrenheit requires multiplication by 9/5 because 5 
    degrees Celsius are the same size as 9 degrees Fahrenheit, but then addition of 32 because 0°C is 32°F. As Figure 3 
    shows, this gives the correct answer of 68 degrees Fahrenheit, obtained in Example 1. The opposite is needed for 
    conversion from Fahrenheit to Celsius, first subtraction of 32, then multiplication by 5/9. The + and ), 
    functions automatically carry out these calculations. 
     
     Figure 3 
       
    						
    							 
    hp calculators 
     
    HP 35s  Temperature Conversions 
     
    hp calculators - 4 - HP 35s  Temperature Conversions - Version 1.0 
    As opposed to a temperature measurement, a temperature difference of zero really is zero, and does not need the 
    addition or subtraction of 32. Adding 5 Celsius degrees to 20°C is the same as adding 9 Fahrenheit degrees to 68°F and 
    does not require addition or subtraction of 32. 
     
    Note: To make clear the distinction between temperature measurement and temperature difference, temperature 
    measurements are usually called “degrees Celsius” or “degrees Fahrenheit”, and temperature differences are called 
    “Celsius degrees” or “Fahrenheit degrees”. 
     
    Because the + and ), functions convert temperature measurements, not temperature differences, 
    conversion of differences must be dealt with either by a manual conversion, using the factor 5/9,or by the addition of a 
    temperature difference to a temperature only on the same scale. 
     
    Example 3: An experimental new heater is designed to raise the temperature of its surroundings by exactly 20 Celsius 
    degrees and then to turn itself off. If the heater is working correctly, what should the temperature be, in 
    degrees Fahrenheit, after the heater is used in a room initially at a temperature of 50 degrees Fahrenheit? 
     
    Solution: A temperature difference of 20 Celsius degrees is not the same as a temperature of 20 degrees Celsius. A 
    temperature of 20 degrees Celsius is 68 degrees Fahrenheit, as Example 1 showed. The temperature 
    difference can be calculated as 20 times 9 divided by 5, giving 36 Fahrenheit degrees. Adding this to 50 will 
    give 86 degrees Fahrenheit.  Figure 4 shows this calculation in Algebraic mode. 
     
     Figure 4 
     
     Alternatively, the conversion functions can be used to calculate this as follows. 
     
     In RPN mode, type the number 50, and press the right-shifted &key to convert it to Celsius. Then add 
    20 Celsius degrees. Finally convert back to Fahrenheit. 
     
     $1+!14),
     
     In Algebraic mode, set up the conversion to Fahrenheit, then do the conversion of 50 to Celsius, and then 
    add 20. In this case, pressing 2 is again not required to complete the calculation. 
     
     ),+$154!12 
     
     Figure 5 
     
    Answer: As figures 4 and 5 show, the correct answer is 86 degrees Fahrenheit. 
       
    						
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