Using the floor function to separate numbers

I am working on an assignment where I have to list all the numbers from 1-200 whose individual sum is odd (e.g 12 = 1 + 2 = 3 and therefore odd, and shall therefore be placed into an array. I have written the code where I am only testing the numbers from 10:18 just to make sure the concept works on a small scale. The problem I am having is removing the number 11 from my output array. With the code I have written, it does not make sense to me why the 11 still remains. Please can someone assist.

 a = 0;

 for k = 10:18;
 a = a + 1;
 initial = k / 10;
 initial2 = floor(initial);
 secondary = (initial - initial2)*10;
 outcome = secondary + initial2;

 if mod(outcome,2) ~=0
  arrayinitialodd(a) = [k]
  end
end

///////////////////////////////

output:

arrayinitialodd =

   10   11   12    0   14    0   16    0   18

///////////////////////////////////////

Proof of operation I get in the command window with respect to the number 11:

a = 2

initial = 1.1000

initial2 = 1

secondary = 1.0000

outcome = 2.0000

value = 11

arrayinitialodd =

   10   11

Answer 1

[Roger Stafford]

Your mistake occurs at the line:

   secondary = (initial - initial2)*10;

You should have written

   Secondary = k - initial2*10;

The quantity initial = k/10 is a number your computer, which is using binary floating point representation, cannot represent precisely. It must necessary have a very tiny error. When you multiply back again by 10, the result is a tiny bit off from an exact integer, so the test

   mod(outcome,2) ~=0

comes out true even though 'outcome' in this case is very close to 2. If you look at an exact value for it, you will discover that.

[dillon-harris]

Thank you for the timely response. I did not even know of the error associated with binary floating point representation.Makes sense now why it was true for ~=0. I can now factor this into future calculations.

Answer 2

[Star Strider]

You’re experiencing floating-point approximation error. You can see that if you change to format long E and remove the semicolon from your ‘outcome’ assignment.

Solution: use mod or rem for secondary instead:

secondary = rem(k,10);

Also, put the ‘a’ increment inside the if block.

[dillon-harris]

Thank you for the timely response. I did change the format to long E, and it provided a good visual with what was happening with the floating-point approximation error. Also moving the 'a' increment inside the if statement was great as it got rid of the zeroes in the matrix, when previously i would write an additional line of code to do so.