Question

With 3-digit rounding after each operation find the value of:

a. 0.4 + 0.4 + … + 0.4 + 100 (where the 0.4 is repeated 100 times)

b. 100+0.4 + 0.4 + … + 0.4 (where the 0.4 is repeated 100 times)

c. Find the absolute and relative error in parts a and b.

Answer 1

In both cases we are getting absolute error as zero.

After adding 0.4 100 times we are getting 40

sum=sum+100   140

absolute error=after rounding value-approximation value

                        140-140

                        =0

relative error=(absolute error)/after rounding value i.e,0

see below c code for better understanding.

#include<stdio.h>
#include<math.h>
main()
{
    int i,aerror,rerror,rvalue;
    float pre=0.4,val=100.0;
    float sum=0.0;
    for(i=1;i<=100;i++){
        sum=sum+pre;
        }
    sum=sum+100;
    printf("%f\n",sum);
        rvalue=round(sum);
    printf("%f..%f\n",sum,(float)rvalue);
    aerror=rvalue-sum;
    rerror=aerror/rvalue;
    printf("a problem:%f..%.f",(float)aerror,(float)rerror);

}