I noticed a difference with round() at 15 decimal places, and I need to know why this is so.

Yesterday, I noticed that

round(2.4999999999999999) %15 decimal places
ans =
3

But

round(2.499999999999999) %16 decimal places
ans =
2

This can be for any number, not just 2. Does anybody know what causes this?

[Jan]

The first example has 16 digits and the 2nd one 15 digits, not the other way around.

Answer 1

[Mara Gati]

It's OK, I found the answer. Floating point doubles are precise to 15dp only.

Wikipedia page

[John D'Errico]

It is not 15 decimal digits that matters, since doubles are not stored in decimal form. A double in MATLAB is actually stored in binary. So 52 binary bits represents something a little more accurate than 15 decimal digits.