c# - Precision of double after decimal point

Question

In the lunch break we started debating about the precision of the double value type.

My colleague thinks, it always has 15 places after the decimal point.

In my opinion one can't tell, because IEEE 754 does not make assumptions about this and it depends on where the first 1 is in the binary representation. (i.e. the size of the number before the decimal point counts, too)

How can one make a more qualified statement?

Answer 1

You're both wrong. A normal double has 53 bits of precision. That's roughly equivalent to 16 decimal digits, but thinking of double values as though they were decimals leads to no end of confusion, and is best avoided.

That said, you are much closer to correct than your colleague--the precision is relative to the value being represented; sufficiently large doubles have no fractional digits of precision.

For example, the next double larger than 4503599627370496.0 is 4503599627370497.0.