Place Value

Our Number System is based on ten.
Using only ten symbols (called Digits) we can write any number.

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

You can use these on their own to count up to 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 (called "units"):

Tens
Units
1 2
ten balls one ball one ball
The Number "12"

So we know that we have 1 Ten and 2 Ones, which makes 12.

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

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

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

So we know that we have 1 Hundred, 4 Tens and 3 Ones

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

Example: "369" means 3 Hundreds, 6 Tens and 9 Units, which is also 3×100 + 6×10 + 9×1

And So On ...

So, each time we need 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!

Zero

What if we have 1 Ten, but no Units? We show that we have no units by using a zero there:

Tens
Units
1 0
ten balls  
The Number "10"

We have to put a zero, or "10" would look like "1".

We use the same thing to show zero tens, hundreds, etc

Example: "203" means 2 Hundreds, Zero Tens and 3 Units.

Names for Each Column

These are the names of each column:

Millions Hundred-Thousands
Ten-Thousands
Thousands
Hundreds
Tens
Units

(For bigger amounts, see Metric Numbers)

Example:

In a place-value table write down the number eleven thousand, three hundred and twenty seven:

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