Table 1 of the BIPM Brochure lists "base" *units* of the SI. Tables 2, 3, and 4 list particular SI "derived" *units*.
However, Tables 6, 7, 8, 9, and 10 list "non-SI" *units* some of which are, nevertheless, "a part of the modern metric system" (my phrase), i.e. are "accepted for use with" the SI (e.g. hour, liter, tonne, etc. in Table 6), and some of which are not a part of the SI nor of the modern metric system. I have no problem explaining to interested persons that the liter is accepted internationally for use with SI Units even though the liter is technically a non-SI unit; and ignoring the distinction for members of the general public. My recommendations are close to those of Terry Simpson. Gene.
