# 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":

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

0 | |

1 | |

2 | |

3 | |

4 | |

5 | |

6 | |

7 | |

8 | |

9 | |

?? |

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").

So we write:

10 |

### Example: this is how we write down **twelve**:

Tens | Ones |

1 | 2 |

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 |

## Zero

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

Tens | Ones |

1 | 0 |

We have to put a Zero in the Ones place or "10" looks 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 |

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

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

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

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

We 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 |

## 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 |