# 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:

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 |

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 |

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 |

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 |