### Introduction

Thousands | Hundreds | Tens | Units | Decimal Point | Tenths | Hundredths | Thousandths |

Th | H | T | U | ● | t | h | th |

You can see that each column in our place value table is worth ten times as much as the column on its right.

For example the Hundreds column is worth 10 times the Tens column (x10). And the opposite is also true – the Tens column is worth ten times less than the Hundreds column (÷10).

Knowing this allows us to be able to quickly multiply and divide by 10, 100 and 1000.

### Multiplying by 10, 100 and 1000

The table below shows what happens to the number 65 when it is multiplied by 10, 100 and 1000:

TTh | Th | H | T | U | t | ||

65 | 6 | 5 | ● | ||||

65 x 10 | 6 | 5 | 0 | ● | |||

65 x 100 | 6 | 5 | 0 | 0 | ● | ||

65 x 1000 | 6 | 5 | 0 | 0 | 0 | ● |

Do you see what happens to 65 when it is multiplied by 10? We are just moving all the digits along one column to the left – because moving along one column increases the numbers value 10 times. Another way to look at this is that we are just adding the 0 from 10 on to the end of 65 to get 650.

Look what happens when we multiply by 100, all the digits move two columns to the left. This increases the numbers value 100 times. We could also say we are adding the two zeroes from 100 on to the end of 65 yo get 6500.

When multiplying by 1000 we move all the digits across 3 columnsto the left, this increases the value of the number 1000 times. We could also say we are adding the three zeroes from 1000 on to the end of 65 to get 65000.

Example 1 (x10)

Question what is 23.5 x 10?

Remember multiplying by 10 is easy. To multiply any number by 10 you just move all the digits one column to the **left**.

Let’s look at this in the place value table. First we put 23.5 in to the correct columns:

Hundreds | Tens | Units | Tenths | |

2 | 3 | ● | 5 |

Next, because we are multiplying by 10, move the digits one column to the left:

Hundreds | Tens | Units | Tenths | |

2 | 3 | 5 | ● |

Now we can see the answer is **235**

Example 2 (x100)

Question: What is 2181 x 100?

To multiply a number by **100** we move all the digits in the number left by **two** columns, another way to look at this is we add the 2 zeroes from 100 on to the end of the number:

218100

Example 3 (x1000)

Question: What is 28 x 1000?

To multiply a number by **1000** we move all the digits in the number left by **three** columns, another way to do this is to add the 3 zeroes from 1000 on to the end of our number:

28000

### Dividing by 10, 100 and 1000

To divide a number by **10** all the digits in our number must move **one** place to the **right**.

To divide a number by **100** all the digits in our number must move **two** places to the **right**.

To divide a number by **1000** all the digits in our number must move **three** places to the **right**.

The table below shows what happens to the number 65 when it is divided by 10, 100 and 1000:

T | U | t | h | th | ||

65 | 6 | 5 | ● | |||

65 ÷ 10 | 6 | ● | 5 | |||

65 ÷ 100 | 0 | ● | 6 | 5 | ||

65 ÷ 1000 | 0 | ● | 0 | 6 | 5 |

Example 1 (÷10)

Question: What is 47.5 ÷ 10?

Let’s look at 47.5 in a place value table:

Tens | Units | Tenths | Hundredths | |

4 | 7 | ● | 5 |

To divide by 10 we just move all the digits one place to the right:

Tens | Units | Tenths | Hundredths | |

4 | ● | 7 | 5 |

We get the answer **4.75**

Example 2 (÷100)

Question: What is 2300 ÷ 100?

When dividing by 100 we move the decimal point two places to the left, so our answer is:

Example 3 (÷1000)

Question: What is 467 ÷ 1000?

When dividing by 1000 we move the decimal point three places to the left, so our answer is: