Memory aids: from kilo up, every step is ×1000 and the symbols are capitals (except k). From milli down, every step is ÷1000 and the symbols are lower case. Only hecto, deca, deci and centi break the 103 pattern.
Greek/Latin roots: kilo (thousand), mega (great), giga (giant), tera (monster), peta/exa (5th/6th power of 1000), zetta/yotta (7th/8th, from Latin/Greek "seven"/"eight"); milli (thousandth), micro (small), nano (dwarf), pico (small amount), femto/atto (Danish 15/18), zepto/yocto (7th/8th again).