The following calculation explains how to convert 0.1 in decimal notation to the binary number.
1/10 = 1.6/16
= 1/16 + 0.6/16
= 1/16 + 1.2/32
= 1/16 + 1/32 + 0.2/32
= 1/16 + 1/32 + 1.6/256
= 1/16 + 1/32 + 1/256 + 1/512 + 1/4096 + 1/8192 + ....
= 2-4 + 2-5 + 2-8 + 2-9 + 2-12 + 2-13 +....
So 0.1 in decimal notation is 0.000110011001100...in binary notation.