Help regarding "format long"

i am trying to solve a=(4:0.0002:4.20) with format long, but i am getting weird values and not accurated ones like 4.196000000000001 4.196200000000000 4.196400000000001 4.196600000000000 4.196800000000001

But it should be like this 4.196000000000000 4.196200000000000 4.196400000000000 4.196600000000000 4.196800000000000

why matlab is not giving me accurate answer and adding 0.000000000000001 at alternative figures.

Answer 1

[Matt Tearle]

Welcome to the joy of round-off error. 0.0002 is not exactly representable in binary, hence adding these floating point numbers causes error at the level of machine precision. Enter eps(4) to see what machine precision is for these values.

Answer 2

[Jiro Doke]

Take a look at this FAQ.

Answer 3

[James Tursa]

You may also find the num2strexact utility to be of some help in understanding this. e.g.,

>> num2strexact(4.196)
ans =
4.1959999999999997299937604111619293689727783203125
>> num2strexact(4.1962)
ans =
4.19620000000000015205614545266143977642059326171875

>>

You can find the num2strexact utility here:

http://www.mathworks.com/matlabcentral/fileexchange/22239-num2strexact-exact-version-of-num2str