In fact, 1/26=0.0384615[384615]… 384615 as a decimal cycle section. So I doubt the value of BigFloat(1/26) and 1/26 giving by Julia are not correct. What happened？

Yes or BigFloat(1//26) which takes the exact rational 1//26 and converts it to BigFloat.

I’m going to assume there are no bugs in the Intel/AMD chips etc, so the number it gives must be the closest 64 bit binary floating point number to the correct value. Let’s see:

You usually want to use prevfloat/nextfloat, eps is the maximum of the distances to the two adjacent floating point numbers, which is not always the same between the two of them (otherwise it’d be the same for all numbers)