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SIGNIFICANT DIGITS - h1014v1_74

Mathematics Volume 1 of 2
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Review of Introductory Mathematics SIGNIFICANT DIGITS SIGNIFICANT DIGITS This  chapter  presents  the  concept  of  significant  digits  and  the  application  of significant digits in a calculation. EO 1.8 DETERMINE  the  number   of  significant  digits  in  a  given number. EO 1.9 Given    a    formula,    CALCULATE    the    answer    with    the appropriate number of significant digits. Calculator Usage, Special Keys Most calculators can be set up to display a fixed number of decimal places. In doing so, the  calculator  continues  to  perform  all  of  its  internal  calculations  using  its  maximum number of places, but rounds the displayed number to the specified number of places. INV key To fix the decimal place press the INV key and the number of the decimal places desired.   For example, to display 2 decimal places, enter INV 2. Significant Digits When numbers are used to represent a measured physical quantity, there is uncertainty associated with  them.   In  performing  arithmetic  operations  with  these  numbers,  this  uncertainty  must  be taken into account.  For example, an automobile odometer measures distance to the nearest 1/10 of a mile.   How can a distance measured on an odometer be added to a distance measured by a survey  which  is  known  to  be  exact  to  the  nearest  1/1000  of  a  mile?  In  order  to  take  this uncertainty into account, we have to realize that we can be only as precise as the least precise number.   Therefore, the number of significant digits must be determined. Suppose the example above is used, and one adds 3.872 miles determined by survey to 2.2 miles obtained from an automobile odometer.   This would sum to 3.872 + 2.2 = 6.072 miles, but the last  two digits  are  not reliable.   Thus  the  answer is  rounded to  6.1  miles.   Since all  we know about the 2.2 miles is that it is more than 2.1 and less than 2.3, we certainly don’t know the sum to any better accuracy.   A single digit to the right is written to denote this accuracy. Rev. 0 Page 53 MA-01







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