Notation of natural numbers

Natural numbers are the numbers we use to count separate objects:

1,\,2,\,3,\,\ldots

. Every natural number has a next one (add 1); the set of natural numbers is infinite. We write them with Hindu–Arabic numerals

0,\,1,\,2,\,\ldots,\,9

(digit 0 is needed for place-value notation, but “0 objects” is not used when you start counting from 1). Place-value system: a digit’s value depends on its place (ones, tens, hundreds, then ones of thousands, ten thousands…). To read large numbers, the digits are grouped in periods of three from right to left: ones period, thousands period, millions period, and so on. In print, people often leave a space (or comma) between periods.

Natural numbers for counting:

1,\,2,\,3,\,\ldots

A digit’s place — ones, tens, hundreds, …

Three places in a row form a period (ones, thousands, millions)

A number can be expanded as a sum of “period × power of 1000”

Hundreds, tens, ones

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