0.1 float is greater than 0.1 double. I expected it to be false

Question

Let:

double d = 0.1;
float f = 0.1;

should the expression

(f > d)

return true or false?

Empirically, the answer is true. However, I expected it to be false.

As 0.1 cannot be perfectly represented in binary, while double has 15 to 16 decimal digits of precision, and float has only 7. So, they both are less than 0.1, while the double is more close to 0.1.

I need an exact explanation for the true.

Answer 1

I'd say the answer depends on the rounding mode when converting the double to float. float has 24 binary bits of precision, and double has 53. In binary, 0.1 is:

0.1₁₀ = 0.0001100110011001100110011001100110011001100110011…₂
             ^        ^         ^   ^ 
             1       10        20  24

So if we round up at the 24th digit, we'll get

0.1₁₀ ~ 0.000110011001100110011001101

which is greater than the exact value and the more precise approximation at 53 digits.