to perform one of the first functions, simply press the key. To perform one of the second functions, you’ll need to press them key and then press the  key  for  the  function  you  wish  to  perform. INSTRUCTION   MANUAL Every  calculator  on  the  market  should  have an  instruction  manual  enclosed  with  it.  Check  out all the features and functions summarized in the instruction manual to become familiar with what your  calculator  will  (and  will  not)  do  for  you. HINTS  ON  COMPUTING It   is   a   general   rule   that   when   you   are expressing  dimensions,  you  express  all  dimensions with  the  same  precision.  Suppose,  for  example, you have a triangle with sides 15.75, 19.30, and 11.20  ft  long.  It  would  be  incorrect  to  express these as 15.75, 19.3, and 11.2 ft, even though the numerical values of 19.3 and 11.2 are the same as  those  of  19.30  and  11.20. It  is  another  general  rule  that  it  is  useless to  work  computations  to  a  precision  that  is higher  than  that  of  the  values  applied  in  the computations.   Suppose,   for   example,   you   are solving a right triangle for the length of side a, using the Pythagorean theorem. Side b is given as 16.5 ft, and side c, as 20.5 ft. By the theorem you  know  that  side  a  equals  the  square  root  of (20.5² –  16.5²),  or  the  square  root  of  148.0.  You could  carry  the  square  root  of  148.0  to  a  large number of decimal places. However, any number beyond two decimal places to the right would be useless,  and  the  second  number  would  be determined only for the purpose of rounding off the first. The  square  root  of  148.0,  to  two  decimal places,  is  12.16.  As  the  0.16  represents  more  than one-half of the difference between 0.10 and 0.20, you round off at 0.2, and call the length of side a 12.2 ft. If the hundredth digit had represented less than one-half of the difference between 0.10 and  0.20,  you  would  have  rounded  off  at  the lower tenth digit, and called the length of side a 12.1 ft. Suppose   that   the   hundredth   digit   had represented one-half of the difference betwveen 0.10 and 0.20, as in 12.15. Some computers in a case  of  this  kind  always  round  off  at  the  lower figure,  as,  12.1.  Others  round  off  at  the  higher figure,   as 12.2.   Better   balanced   results   are usually obtained by rounding off at the nearest even figure. By this rule, 12.25 would round off at  12.2,  but  12.35  would  round  off  at  12.4. UNITS  OF  MEASUREMENT Engineering  science  would  not  be  so  precise as it is today if it did not make use of systems of measurement. In  fieldwork,  drafting,  office computation,  scheduling,  and  quality  control,  it is important to be able to measure accurately the magnitudes  of  the  various  variables  necessary  for engineering   computations,   such   as   directions, distances, materials, work, passage of time, and many  other  things. The  art  of  measuring  is  fundamental  in  all fields of engineering and even in our daily lives. We  are  familiar,  for  instance,  with  “gallons,” which determines the amount of gasoline we put in  our  car  and  with  “miles,”  which  tells  us  the distance  we  have  to  drive  to  and  from  work.  It is also interesting to note that the development of  most  of  these  standard  units  of  measure parallels  the  development  of  civilization  itself,  for there has always been a need for measurement. In the early days, people used night and day and the cycle of the four seasons as their measure of time. The units of linear measure were initially adopted  as  comparison  to  the  dimensions  of various  parts  of  a  man’s  body.  For  example,  a “digit”   was  at  that  time  the  width  of  a  man’s middle  finger,  and  a  “palm”  was  the  breadth  of an  open  hand.  The  same  applies  to  most  other units of linear measure that we know today—like the  “foot,”  the  “pace,”  and  the  “fathom.”  The only difference between today’s units of measure and those of olden days is that those of today are standardized.  It  is  with  the  standard  types  of measurements  that  we  are  concerned  in  this training manual. At  present,  two  units  of  measurement  are used throughout the world. They are the English system and the metric system, Many nations use the metric system. The metric system is the most practical method of  measurement,  for  it  is  based  on  the  decimal system, in which units differ in size by multiples of tens, like the U.S. monetary system in which 10 mills equal 1 cent; 100 mills or 10 cents equal 1 dime; and 1,000 mills, 100 cents, or 10 dimes equal one dollar. When we perform computations with  multiples  of  10,  it  is  convenient  to  use  an exponential  method  of  expression  as  you  may recall  from  your  study  of  mathematics. 1-26