Question

I am learning Objective-C and have completed a simple program and got an unexpected result. This program is just a multiplication table test… User inputs the number of iterations(test questions), then inputs answers. That after program displays the number of right and wrong answers, percentage and accepted/failed result.

#import <Foundation/Foundation.h>

int main (int argc, const char * argv[])
{

NSAutoreleasePool * pool = [[NSAutoreleasePool alloc] init];
NSLog(@"Welcome to multiplication table test");
int rightAnswers; //the sum of the right answers
int wrongAnswers; //the sum of wrong answers
int combinations; //the number of combinations@


NSLog(@"Please, input the number of test combinations");
scanf("%d",&combinations);

for(int i=0; i<combinations; ++i)
{
    int firstInt=rand()%8+1;
    int secondInt=rand()%8+1;
    int result=firstInt*secondInt;
    int answer;


    NSLog(@"%d*%d=",firstInt,secondInt);
    scanf("%d",&answer);
    if(answer==result)
    {
        NSLog(@"Ok");
        rightAnswers++;
    }
    else
    {
        NSLog(@"Error");
        wrongAnswers++;
    }
}
int percent=(100/combinations)*rightAnswers;
NSLog(@"Combinations passed: %d",combinations);
NSLog(@"Answered right: %d times",rightAnswers);
NSLog(@"Answered wrong: %d times",wrongAnswers);
NSLog(@"Completed %d percent",percent);
if(percent>=70)NSLog(@"accepted");
else
    NSLog(@"failed");
[pool drain];
return 0;

}

Problem (strange result)

When I input 3 iterations and answer ’em right, i am not getting of 100% right. Getting only
99%. The same count I tried on my iPhone calculator.

100 / 3 = 33.3333333… percentage for one right answer (program displays 33%. The digits after mantissa getting cut off)

33.3333333… * 3=100%

Can someone explain me where I went wrong? Thanx.

Answer 1

This is a result of integer division. When you perform division between two integer types, the result is automatically rounded towards 0 to form an integer. So, integer division of (100 / 3) gives a result of 33, not 33.33…. When you multiply that by 3, you get 99. To fix this, you can force floating point division by changing 100 to 100.0. The .0 tells the compiler that it should use a floating point type instead of an integer, forcing floating point division. As a result, rounding will not occur after the division. However, 33.33… cannot be represented exactly by binary numbers. Because of this, you may still see incorrect results at times. Since you store the result as an integer, rounding down will still occur after the multiplication, which will make it more obvious. If you want to use an integer type, you should use the round function on the result:

int percent = round((100.0 / combinations) * rightAnswers);

This will cause the number to be rounded to the closest integer before converting it to an integer type. Alternately, you could use a floating point storage type and specify a certain number of decimal places to display:

float percent = (100.0 / combinations) * rightAnswers;
NSLog(@"Completed %.1f percent",percent); // Display result with 1 decimal place

Finally, since floating point math will still cause rounding for numbers that can’t be represented in binary, I would suggest multiplying by rightAnswers before dividing by combinations. This will increase the chances that the result is representable. For example, 100/3=33.33… is not representable and will be rounded. If you multiply by 3 first, you get 300/3=100, which is representable and will not be rounded.