Binary is represented in powers of 2. 1/9 is a (decimal) fraction. You would convert this into a sum of binary fractions
1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128
To help identify which bit positions, first, as an example, compute 2^n / 9, where n is the number + 1 of significant bits of the precision of the result you want. Then look at the binary result and then place the binary decimal point to the left n bits. You can use the Programmer view of the Windows Calculator or locate one on the web. In Programmers view
For 32-bit fraction with decimal selected, enter: 1, Lsh, 32, =
Result: 4294967296 (decimal), 100000000000000000000000000000000 (binary)
Enter (in decimal mode): /, 9, =
Result: 477218588 (decimal), 00011100011100011100011100011100 (binary)
Insert "." 32 places to left of right most bit: .00011100011100011100011100011100
As how to represent this in "floating point format", you will have to decide what format. There are many different formats that are used.
In anticipation of you asking....
15/9ths can be calculated with the Windows Calculator (32 bits)
1, Lsh, 32, *, 15, /, 9
Result: 7158278826 (decimal), 110101010101010101010101010101010 (binary)
Float decimal point 32 positions to left: 1.10101010101010101010101010101010