How does 6.022140857*10^23 differ from 6.022140857e+23?

In matlab if I write the following script I get a non-zero answer which is awkward, can somebody please explain this?

 av = 6.022140857*10^23;
 av_1 = 6.022140857e+23;
 diff = av - av_1

The answer I get is

 diff =

   -67108864

Answer 1

[Stephen23]

>> fprintf('%.0f\n',av)
602214085699999950000000
>> fprintf('%.0f\n',av_1)
602214085700000020000000

because X*B^P performs two numeric operations on three floating point values and accumulates floating point error with each operation. XeP generates the value directly, without any numeric operations.

Because of this:

https://www.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero

http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

https://www.mathworks.com/matlabcentral/answers/41536-why-is-2-24-10-22-4-not-equal-to-0

Or any of the thousand other threads explaining floating point errors and how they accumulate during numeric operations.

You might also be interested in trying James Tursa's excellent FEX submission:

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

[Antonius Armanious]

Thanks for the clarification.