Decimal arithmetic

• For computer calculation, we solve the arithmetic problem by using only finite decimals

• But then the 1/3 problem is even worse:

        #include <stdio.h>

        int main(void) {
          unsigned i;
          double total = 0;

          for (i=0; i < 300; i++) 
            total += 1.0/3.0;

          printf("%.20f\n", total);
          return 0;
        }

• The output:

        99.99999999999965893949

• (The computer is using binary expansions, not decimal expansions)

  • (But the problem is just the same.)