Ten Times Bigger

Ten ones make a ten. Ten tens make a hundred. Ten hundreds make a thousand. The pattern never stops.

Every place is ten times the next

Moving one place to the left multiplies the value by ten. Moving right divides it by ten.

A digit and its value are different

In 3,500 the digit 3 is worth 3,000, and in 350 the same digit 3 is worth only 300.

This one idea is what makes every algorithm in this year work.

One rule generates the whole system

Each place is worth ten times the place to its right: ones, tens, hundreds, thousands, ten thousands. The pattern never stops and never changes. Ten of anything bundles into one of the next thing up, which is why the columns march leftwards in a perfectly regular way.

The same digit, ten times the value

In 4,400 the two 4s look identical but the left one is worth 4,000 and the right one 400. The left is ten times the right, because it sits one place further left. Position is doing all the work; the digit only says how many.

The rule works in both directions

Going left multiplies by ten; going right divides by ten. A hundred is a tenth of a thousand. Reading the rule rightwards is what will let you continue past the ones place into tenths and hundredths later this year — the pattern simply keeps going.

Why ten, and not some other number

There is nothing mathematically special about ten; we use it because people have ten fingers. Computers bundle in twos and get along fine. Knowing our system is a choice rather than a law makes the bundling rule easier to see as a rule.