Place Value

We write numbers using only ten symbols (called Digits).
Where we place them is important.

The Ten Digits

The Digits we use today are called "Hindu-Arabic Numerals" and look like these:

0   1   2   3   4   5   6   7   8   9


We can use these on their own to count up to 9:

0  
1 one ball
2 one ballone ball
3 one ballone ballone ball
4 one ballone ballone ballone ball
5 one ballone ballone ballone ballone ball
6 one ballone ballone ballone ballone ballone ball
7 one ballone ballone ballone ballone ballone ballone ball
8 one ballone ballone ballone ballone ballone ballone ballone ball
9 one ballone ballone ballone ballone ballone ballone ballone ballone ball
?? one ballone ballone ballone ballone ballone ballone ballone ballone ballone ball

But what happens after 9?

Ten Or More ...

When we have more than 9 items, we start another column - the "tens" column - and we write down how many "tens" we have, followed by how many "ones" (also called "units").

Example: this is how we write down twelve:

Tens
Ones
1 2
ten balls one ballone ball
The Number "12"

It says we have 1 Ten and 2 Ones, which makes 12.

This can also be written as 1 × 10 + 2 × 1.

Example: "35" means 3 Tens and 5 Ones, which is also 3 × 10 + 5 × 1

Tens
Ones
3 5
ten ballsten ballsten balls one ballone ballone ballone ballone ball
The Number "35"

Zero

What if we have 1 Ten, but no Ones? We show "no Ones" by putting a zero there:

Tens
Ones
1 0
ten balls  
The Number "10"

We have to put a zero in the Ones place, or "10" would look like "1".

A Hundred Or More ...

When we have more than 99 items, we start another column - the "hundreds" column. Now we need to show how many Hundreds, Tens and Ones:

Hundreds
Tens
Ones
1 4 3
ten balls ten ballsten ballsten ballsten balls one ball one ball one ball
The Number 143

That shows we have 1 Hundred, 4 Tens and 3 Ones:

  • The Place Value of the "1" is 100
  • The Place Value of the "4" is 40
  • The Place Value of the "3" is 3

This can also be written as 1 × 100 + 4 × 10 + 3 × 1.

Example: "369" means 3 Hundreds, 6 Tens and 9 Ones

  • The Place Value of the "3" is 300
  • The Place Value of the "6" is 60
  • The Place Value of the "9" is 9

Which is also 3 × 100 + 6 × 10 + 9 × 1

We can also use a Zero when there are no Tens:

Example: "104" means 1 Hundred, Zero Tens and 4 Ones.

Hundreds
Tens
Ones
1 0 4
ten balls   one ballone ballone ballone ball
The Number 104

And So On ...

Each time we want to show a bigger number we just add one column to the left and we know it is always 10 times bigger than than the column on its right.

each new column on the left is ten times bigger

So, where we PLACE a digit is important!

Names for Each Column

These are the names of each column:

Millions Hundred-Thousands
Ten-Thousands
Thousands
Hundreds
Tens
Ones

(For bigger amounts, see Metric Numbers)

Example: The number eleven thousand, three hundred and twenty seven in a place value table:

Ten-Thousands
Thousands
Hundreds
Tens
Ones
1 1 3 2 7
The Number 11,327