Numerical Method for Civil and Production

Hi Teacher, 

The last question in the quiz no 0.004% has only one significant figure. how can we detect the least from those choices. 

^{1, finite precision: is decimal representation of a number which has been rounded or truncated. There many cases where this may be necessary or appropriate. For example 1/3 and the transcendental numbers e and π all have infinite decimal representations.}

2, List the source of error: generally there are two types of error based on their sources.

non-numerical errors  their sources of errors are errors in the mathematical model and input data and numerical errors their sources of errors are truncation errors and round-off errors.

3, Define error measurements:there are two error measurements,

Those are absolute error: is the magnitude of the difference between the true value x and the approximate value xa. The error between two values is defined as abs = kx − xak , where x denotes the exact value and xa denotes the approximation. And

The relative error is defined as rel = kx − xak kxk . which assumes x 6= 0; otherwise relative error is not defined.

4, Define mathematical modeling

  mathematical model:  is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling.

5, Define Accuracy and precision

   Accuracy:refers to how closely a value agrees with the true value. 

   precision:refers to how closely values agrees with each other.

6, change 35.625 in to binary system 

35.625 is changed to binary as : first we convert the integer part

(35)10 to ( )2

     35/2  =   17  put here the reminder   1

    17/2  =     8       >>                >>          1

     8/2   =      4       >>               >>           0

     4/2    =      2       >>               >>           0

      2/2    =     1        >>              >>           0

                                                                    1

     collects the reminders up wards  here:(35)10  =(100011)2

Secondly converts the fraction part

   (0.625)10 to ( )2

    0.625*2   = 1.25  put also here the integer part    1

    0.25*2     =0.5     >>                       >>                   0

     0.5*2       =  1      >>                       >>                    1

     collect down ward  (0.625)10   =   (101)2 

    The final result is  (35.625)10  =  (100011.101)2