Here are some sample conversions
0.1₁₀ = 0.00011001100110011001100110011001…₂
0.01₁₀ = 0.00000010100011110101110000101000…₂
0.001₁₀ = 0.00000000010000011000100100110111…₂
0.0001₁₀ = 0.00000000000001101000110110111000…₂
0.00001₁₀ = 0.00000000000000001010001111010111…₂
0.000001₁₀ = 0.00000000000000000000100001100010…₂
There doesn't appear to be any reasonable repeating pattern for these. As well, the decimal would need to be shifted to the right by some finite amount with an infinite number of zeros to the left.
It seems like it fails to communicate anything after base conversion.
Or similarly, If you went to base 100, how would you communicate half as many zeros.

