MATLAB: How to fix the digits for the summation

digitsroundingsummation

Dear All, I have a code that finds the percentage of each case from the total population, I have 10 cases and the summation of their percentages must be 100% or 0 for example, but the problem is that I am still getting a summation of 100.01 or 99.99 or 99.98, what is the reason here and how can I fix it please, Notice: I rounded the results into 2 digits before I calculate the summation.

Best Answer

See the documentation section on Floating-Point Numbers (link). You are most likely seeing the result of floating-point approximation error. Also, rounding the numbers first loses precision, and likely results in the inaccuracies you get. The solution is not to round the intermediate values, only the results, and the only if necessary.

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MATLAB: Extracting a specific digit from a float w/o floating-point implementation rounding issues

Some people will incorrectly tell you that this is not possible, but in reality there is a simple and efficient solution:

>> N = 130404809.288;
>> mod(round(10000*N),10)
ans =  0
>> N = 130404809.2882;
>> mod(round(10000*N),10)
ans =  2
>> N = 136147309.434;
>> mod(round(10000*N),10)
ans =  0

This relies on your statement that the values have "with either three or four digits to the right of the decimal point", i.e. that the fifth digit is zero (the sixth and any further digits, including any floating point error, are totally irrelevant). This means that after multiplying by 10000 (NOT by 1000 as you tried) a simple round will remove all floating point error from the number:

xyz.abcd0err % input
xyzabcd.0err % *10000
xyzabcd      % round
      d      % mod 10

You were almost there, just off by a factor of ten.

MATLAB: Relational operator == doesn’t work properly in some cases!

You are seeing the effects of floating-point approximation error.

See for example: Why is 0.3 - 0.2 - 0.1 (or similar) not equal to zero? and Floating-Point Numbers.

Best Answer

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MATLAB: Extracting a specific digit from a float w/o floating-point implementation rounding issues

MATLAB: Relational operator == doesn’t work properly in some cases!

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