The problem isn't the type, it's the bits. If you convert from Float64, you'll get garbage bits once you go past the bits determined by float64:

    julia> BigFloat(1.1)
    1.100000000000000088817841970012523233890533447265625

I'd recommend using the big string macro though isntead of converting explictly from a string:

    julia> big"1.1"
    1.100000000000000000000000000000000000000000000000000000000000000000000000000003