IEEE 754 Double-Precision and Machine Epsilon

The machine precision using IEEE 754 double-precision is 2^−53 ≈ 1.1102e^−16 since it uses round-off and the significant has 53 bit (1/2 * 2^1-53)

Why in MATLAB the value eps is 2.2204e^-16 but it usees the same standard?

Does that mean that MATLAB can't represent all the numbers like the IEEE 754 but just a part of them?

Answer 1

[Steven Lord]

From this post on Cleve Moler's blog: "Either eps/2 or eps can be called the roundoff level."

You're using eps/2.