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Editorial Team
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Asked: 2026-05-23T08:44:16+00:00

There are two similar matlab programs, one iterates 10 times while another iterates 11

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There are two similar matlab programs, one iterates 10 times while another iterates 11 times.

One:

i = 0;
x = 0.0;
h = 0.1;
while x < 1.0
    i = i + 1;
    x = i * h;
    disp([i,x]);
end

Another:

i = 0;
x = 0.0;
h = 0.1;
while x < 1.0
    i = i + 1;
    x = x + h;
    disp([i,x]);
end

I don’t understand why there is difference between the floating point add operation and the multiple.

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1 Answer

  1. Editorial Team

    Compare the output of the following:

    >> fprintf('%0.20f\n', 0.1.*(1:10))
0.10000000000000001000
0.20000000000000001000
0.30000000000000004000
0.40000000000000002000
0.50000000000000000000
0.60000000000000009000
0.70000000000000007000
0.80000000000000004000
0.90000000000000002000
1.00000000000000000000

>> fprintf('%0.20f\n', cumsum(repmat(0.1,1,10)))
0.10000000000000001000
0.20000000000000001000
0.30000000000000004000
0.40000000000000002000
0.50000000000000000000
0.59999999999999998000
0.69999999999999996000
0.79999999999999993000
0.89999999999999991000
0.99999999999999989000

    Also compare against using MATLAB’s COLON operator:

    >> fprintf('%0.20f\n', 0.1:0.1:1)
0.10000000000000001000
0.20000000000000001000
0.30000000000000004000
0.40000000000000002000
0.50000000000000000000
0.59999999999999998000
0.69999999999999996000
0.80000000000000004000
0.90000000000000002000
1.00000000000000000000

    If you want to see the 64-bit binary representation, use:

    >> format hex
>> [(0.1:0.1:1)' (0.1.*(1:10))' cumsum(repmat(0.1,10,1))]
   3fb999999999999a   3fb999999999999a   3fb999999999999a
   3fc999999999999a   3fc999999999999a   3fc999999999999a
   3fd3333333333334   3fd3333333333334   3fd3333333333334
   3fd999999999999a   3fd999999999999a   3fd999999999999a
   3fe0000000000000   3fe0000000000000   3fe0000000000000
   3fe3333333333333   3fe3333333333334   3fe3333333333333
   3fe6666666666666   3fe6666666666667   3fe6666666666666
   3fe999999999999a   3fe999999999999a   3fe9999999999999
   3feccccccccccccd   3feccccccccccccd   3feccccccccccccc
   3ff0000000000000   3ff0000000000000   3fefffffffffffff

    Some suggested readings (MATLAB related):

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