Zero and Place-Value — Build an Abacus and Count Like the World Does

For most of history there was no zero. Around 628 AD the Indian mathematician Brahmagupta made zero a real number and gave the decimal place-value system its rules. You will build a counting machine that shows how it works.

Make a small frame from card and thread three or four rows of beads across it (or just lay out rows of beads in columns on the table). Label the columns from the right: ones, tens, hundreds, thousands. Each column is worth ten times the one to its right.

Show the number 305: put 3 beads in the hundreds column, NONE in the tens, and 5 in the ones. The empty tens column is the job of zero -- without it, 35 and 305 would look the same. Practise a few numbers, sliding beads and reading them off. Try adding by sliding beads and 'carrying' to the next column when one fills up.

What your abacus teaches. (1) In a place-value system a digit's value depends on its COLUMN, each worth ten times the next -- so just ten symbols (0-9) can write any number, however large. (2) Zero does two jobs: it holds an empty column so the others line up, AND it is a number you can calculate with. (3) Roman numerals had neither, which is why calculating with them was so painful -- try multiplying MDCCC by anything. (4) The same positional trick, cut down to just 0 and 1, is how every computer on Earth counts; and zero went on to anchor algebra, coordinates and calculus. It is hard to name a more powerful nothing.