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.