Adjustment Some survey processes are not complete until measurements  are  within  usable  limits  or  until corrections have been applied to these measure- ments  to  distribute  accumulated  errors.  Small errors that are not apparent in individual measure- ments   can   accumulate   to   a   sizeable   amount. Adjusting is the process used to distribute these errors  among  the  many  points  or  stations  until the effect on each point has been reduced to the degree that all measurements are within usable limits. For example, assume that 100 measurements were  made  to  the  nearest  unit  for  the  accuracy required.  This  requires  estimating  the  nearest one-half unit during measurement. At the end of the course, an error of + 4 units results. Adjusting this means each measurement is reduced 0.04 unit. Since  the  measurements  were  read  only  to  the nearest  unit,  this  adjustment  would  not  be measurable at any point, and the adjusted result would  be  correct. SIGNIFICANT FIGURES.— The term signif- icant figures refers to those digits in a number that have meaning; that is, whose values are definitely known  to  be  exact. In   a   measured   quantity,   the   number   of significant figures is determined by the accuracy of   the   measurement.   For   example,   a   roughly measured distance of 193 ft has three significant figures.  More  carefully  measured,  the  same distance, 192.7 ft, has four significant figures. If measured still more accurately, 192.68 ft has five significant  figures. In  surveying,  the  significant  figures  should reflect  the  allowable  error  or  tolerance  in  the measurements. For example, suppose a measure- ment of 941.26 units is made with a probable error of  ±  0.03  unit.  The  ±  0.03  casts  some  doubt  on the fifth digit which can vary from 3 to 9, but the fourth digit will still remain 2. We can say that 941.26 has five significant figures; and from the allowable   error,   we   know   the   fifth   digit   is doubtful.  However,  if  the  probable  error  were ±0.07,  the  fourth  digit  could  be  affected.  The number  could  vary  from  941.19  to  941.33,  and the fourth digit could be read 1, 2, or 3. The fifth digit  in  this  measurement  is  meaningless.  The number  has  only  four  significant  figures  and should be written as such. The  number  of  significant  figures  in  a  number ending  in  one  or  more  zeros  is  unknown  unless more  information  is  given.  The  zeros  may  have been  added  to  show  the  location  of  the  decimal point; for example, 73200 may have three, four, or five significant figures, depending on whether the true value is accurate to 100, 10, or 1 unit(s). If  the  number  is  written  73200.0,  it  indicates accuracy is carried to the tenth of a unit and is considered  to  have  six  significant  figures. When  decimals  are  used,  the  number  of significant  figures  is  not  always  the  number  of digits.  A  zero  may  or  may  not  be  significant, depending  on  its  position  with  respect  to  the decimal  and  the  digits.  As  mentioned  above,  zeros may have been added to show the position of the decimal  point.  Study  the  following  examples: 0.000047 . . . . . . . 0.0100470 . . . . . . . 0.1000470 . . . . . . . 2.0100470 . . . . . . . two  significant  figures six significant figures seven significant figures eight  significant  figures In long computations, the values are carried out to one more digit than required in the result. The  number  is  rounded  off  to  the  required numbers  of  digits  as  a  final  step. ROUNDING OFF NUMBERS.—  Rounding off is the process of dropping one or more digits and  replacing  them  with  zeros,  if  necessary,  to indicate   the   number   of   significant   figures. Numbers  used  in  surveying  are  rounded  off according  to  the  following  rules: 1. When the digit to be dropped is less than 5, the number is written without the digit or any others  that  follow  it.  (Example:  0.054  becomes 0.05.) 2.  When  the  digit  is  equal  to  5,  the  nearest EVEN  number  is  substituted  for  the  preceding digit.  (Examples:  0.055  becomes  0.06;  0.045 becomes   0.04.) 3.  When  the  digit  to  be  dropped  is  greater than  5,  the  preceding  digit  is  increased  by  one. (Example:  0.047  becomes  0.05.) 4.  Dropped  digits  to  the  left  of  the  decimal point  are  replaced  by  zeros. 5. Dropped digits to the right of the decimal points are never replaced. 11-8