Math & History: Whole Numbers: Base Ten Positional Number System & Place Value

I. Whole Number
Whole numbers are the set of natural/counting numbers but with the inclusion of zero.
{0, 1, 2, 3, 4...}

II. Understanding Base Systems
A long time ago, before base systems, there was no convenient way of writing big numbers. So to count one, you'd (using the established symbol of the time) write:

1

To write five, you'd write

11111

And if you wanted eight, would have to write eight notches

11111111

and so on.

To deal with this problem, humans invented number systems. The number system we use is referred to as the Hindu-Arabic numeral system. This system uses as it's base the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Since the number of unique digits in this system is ten, it is referred to as a base 10 system.

As a side note, other societies in history have used other base systems. For instance, the Mayans used a base 20 system and the Babylonians used a base 60 system.

III. Place Value
All numbers in our number system are written using the digits 0 through 9 with the position of the digit in the number determining the value of the digit. Each place has a value 10 times the place to its right. More technically, the value of a digit in a number is a function of its position or place in the numeral. For example, when we write the number 2,364 we mean the sum of

2 Thousands + 3 Hundreds + 6 Tens + 4 Ones

With this number, we find that there are 2 units of a thousand plus 3 units of a hundred plus 6 units of ten plus 4 units of one. Moving from right to left, each unit increases by a power of ten (ten times the previous unit).

Another way of expressing it would be:

2 x 1000 + 3 x 100 + 6 x 10 + 4 x 1

This presentation of the number expresses the important idea that the quantity represented by a digit is the product of its face value and its place value.

Khan: Abacus
Video

IV. Periods
To make large whole numbers easier to read, commas are used to separate the digits into groups of three referred to as periods. Each period has a name such as ones, thousands, millions, billions, and so on.