errors and approximation

 

relative errors

relative error  =

              error                

measurement value

 

percentage error  =

            error                       ×      100   %

measurement value                  1

 

addition of quantities involving errors

measurements are added ; the errors are added;

( a ± b ) + ( c ± d ) = (a + c ) ± ( b + d )

 

multiplication of quantities with errors

find the largest possible value ( M ) and smallest possible value ( m )

calculate their  average     avg   =   ( M + m ) / 2

 

calculate  the error ( e ) by  finding the difference between the average result and the smallest and largest measurements

M — avg =  e

avg — m = e

 

answer  =  avg ± e

 

 

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