how to efficiently storing floating point numbers with limited number

I want to store a set of floating points which have a maximum of 8
digits, sign and decimal point.

i.e
values between -99999999.0 and 99999999.0

e.g.

these would be valid:

-78.2234
6733.2225

these would be invalid and will need to be truncated:

224155.33366 tunc to 224155.33
-52.436627882 tunc to -52.436629

My current scheme will only save a few bytes:

write sign (1 bit)
write decimal point position (3bit)
write digits (variable: 24 - 32 bits)   digits 0-6 = 3 bits, digits
7-9 = 4 bits

so a number would be repsented by between 28 and 36 bits which is very
similar to that of a normal 32bit float...

I may be able to get away with only needing six digit values, however
that will only bring the number of bits needed to between 22 and
28bits which is not a significant saving.

Anyone have any idea of a better way to store such values?

is there a 16 bit or 24 bit floating point scheme?