Thank's a a lot. What I understand from all this (I will explain with an example):

The number 0.20000000000000029 in double precision 0011111111001001100110011001100110011001100110011001100110100100 This is actually the number 0.20000000000000028865798640254070051014423370361328125

In Java( as you explained), this number is 0.2000000000000003. This number is enough to represent. Already in double precision, the number 0.2000000000000003 and the number 0.20000000000000028865798640254070051014423370361328125 is the same(0011111111001001100110011001100110011001100110011001100110100100).

Thus, %.20f will add zero to the number 0.2000000000000003 and print 0.20000000000000030000.

If it were %.15f, it would round the number 0.20000000000000030000 to 15 precision and write 0.200000000000000 on the screen.

If it were %.16f, it would round the number 0.20000000000000030000 to 16 precision and write 0,2000000000000003 on the screen. Right?