There are three different widely accepted systems used to describe the transmissive properties of filters.
One of the systems you have used in your question is called the ND x.x number system and is used by Lee and Tiffen to describe their filters. It is the only system that uses decimals in the notation. The decimal values are based on optical density, not f-stop reduction. An ND 0.3 filter has a one-stop reduction in terms of f-stop, as half the light striking the filter is allowed to pass through. An ND 0.6 has a two-stop reduction as 1/4 of the light passes through. An ND 0.9 rating is a three-stop filter. Each increase of ND 0.3 results in one additional stop of light reduction. So an ND 1.8 is a six-stop filter, while an ND 2.0 is 6 2/3-stop filter, and so on. Note that 0.3 is approximately the Log(base 10) of 2.
The other system referenced in your question, used by Hoya, B+W, and Cokin, is the ND 1/x (or 1/2^x) system. Each filter is described as the reciprocal of the amount of light allowed to pass through the filter. An ND2 allows one-half the light to pass for a one-stop reduction. An ND4 allows one-fourth the light to pass for a two-stop reduction, an ND8 allows 1/8 the light to pass for a 3-stop reduction. An ND64 filter allows 1/64 the light to pass for a six-stop reduction. Note that each increase of one stop in this system is a power of the number "2".
Another system, used by others is the ND1xx notation. All of the numbers begin with a "1" and include two other digits. The second and third digits express the number of stops of light the filter reduces. An ND 101 filter is a one-stop filter, an ND 102 is a two-stop filter, and ND 106 is a six-stop filter, and so on.
To see a chart that shows each system and how filters in one system relate to filters using one of the other notations, please see this chart at wikipedia. This chart also shows the optical density (0.3, 0.6, etc.), f-stop reduction (1-stop, 2-stop, etc.), % transmittance (50%, 25%, etc.), and fractional transmittance (0.5, 0.25, etc), for each step in each system.