What is one thousandth grams?

You just have to use the greek radicals.

So a millionth of a gram is a microgram (ug).

Try to get these other ones:
yocto (10-24) y, zepto (10-21) z, atto (10-18) a, femto (10-15) f, pico (10-12) p, nano (10-9) n, micro (10-6) u, milli (10-3) m, centi (10-2) c, deci (10-1) d, deka (101) daor D, hecto (102) h, kilo (103) k or K, mega (106) M, giga (109) G, tera (1012) T, peta (1015) P, exa (1018) E, zetta (1021) Z, yotta (1024) Y.