WEBS Teachers' Resources ebook_final | Page 467

Name: ___________________________ Group: _____ Date: ________ MEASUREMENT: WORK WITH APPROXIMATIONS (II) To work with approximations is more comfortable but if you don’t work with the exact number, it means you commit some error in your calculations. Whenever you work with approximations you should also measure the error you perpetrate. There are to different ways of measuring error. Absolute Error: It’s the absolute value of the difference between the exact number and its approximation. We write E A. It’s expressed in the same units than the number and its approximation. E A � ExactValue � Approximation � Approximation � ExactValue Examples: � When we approximate � � 3.14we commit an absolute error smaller than one unit of the order of approximation.� E A � 3.141592654...� 3.14 � 0.001592654... � 0.01 � When we approximate � � 3.15we commit an absolute error smaller than one unit of the order of approximation.� E A � 3.15 � 3.14159265... � 0.00840734... � 0.01 Relative Error: It’s the quotient between the absolute error and the exact number. We write E R. We use this formula when we want to determine the grade of precision in the measurement of two or more magnitudes. The relative error is a notdimensional value. E A E R �� Exact Number Discuss in pairs: Who is more imprecise? An engineer that commit an absolute error of 1 cm measuring the width of highway of 200m wide or a dressmaker that commit an absolute error of 0.5 cm measuring the length of a bride dress tail of 1m long? ...................................................................................................................... ................................................................................................................................ ............................................................................................................................. ... ................................................................................................................................