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?
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