Place Value Mastery

The decimal system may be the most successful invention in math. A digit's worth depends on where it sits: the 3 in 300 is worth a hundred times the 3 in 3. This positional notation, carried from India by Arab traders, replaced clumsy Roman numerals and made modern arithmetic possible.

Place value runs rightward too: tenths, then hundredths, then thousandths. The stakes are real — 0.1 grams of a drug versus 1.0 grams is a tenfold gap that can be fatal.