# Why does rem(Centnum,5) give me an answer that is not zero?

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John Jamieson on 27 Oct 2020
Answered: dpb on 27 Oct 2020
I created the following code in order to isolate canadian coins from the value of a cheque:
function [] = Jamiesonlab4 ()
Cheque=input('Enter the value of the cheque to be cashed: ');
Dollar=floor(Cheque);
Cent=Cheque-Dollar;
Centnum=Cent*100;
while (Cheque < 0) || (rem(Centnum,5) ~= 0)
Cheque=input('Input invalid, please enter a cheque value that cent value is divsible by five and non-negative: ');
Centnum=Cent*100;
end
Toonies=floor(Cheque/2);
Toonievalue=Toonies*2;
Remaining=(Cheque-Toonievalue);
Dollar=floor(Remaining);
Quarters=floor(Centnum/25);
Dimes=floor((Centnum-Quarters*25)/10);
Nickels=floor((Centnum-Quarters*25-Dimes*10)/5);
fprintf('The value in coins for this Cheque is:\n ')
if Toonies == 1
fprintf('There is %i toony\n', Toonies)
else
fprintf('There are %i toonies\n', Toonies)
end
if Dollar == 1
fprintf('There is %i Loony\n', Dollar)
else
fprintf('There are %i Loonies\n', Dollar)
end
if Quarters == 1
fprintf('There is %i Quarter\n', Quarters)
else
fprintf('There are %i Quarters\n', Quarters)
end
if Dimes == 1
fprintf('There is %i dime\n', Dimes)
else
fprintf('There are %i Dimes\n', Dimes)
end
if Nickels == 1
fprintf('There is %i nickel\n', Nickels)
else
fprintf('There are %i nickels\n', Nickels)
end
end
However, there is an error that occurs at the while loop. As if I enter an input such as 7.45, it claims it is invalid. Yet the number going into Centnum should be 45, which is divisible by 5. What is wrong here?

Steven Lord on 27 Oct 2020
>> x = 7.45;
>> d = floor(x);
>> c = x-d
c =
0.45
>> cn = 100*c;
>> cn - 45
ans =
1.4210854715202e-14
cn is not exactly forty-five one hundredths. No, this is not a bug. Just as you cannot represent, say, 1/3 as a decimal number exactly with a finite number of digits you also cannot represent 0.45 as a double precision number exactly.
You probably want to round cn before operating on it with the assumption that it contains an integer value.

dpb on 27 Oct 2020
>> format long,format compact
>> rem(Centnum,5)
ans =
1.421085471520200e-14
>>
0.05 cannot be stored exactly in floating point; hence rounding has bit you.
You'll need to round() your cent values to convert to exact integers.

R2019b

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