# 1.03 Order numbers

Lesson

## Ideas

Before we try and order 5-digit numbers, let's check we know how to  read and write  them.

### Examples

#### Example 1

Write the following using numerals:

fifty thousand, five hundred and fifty five

Worked Solution
Create a strategy

Write the number in a place value table.

Apply the idea

In numerals, fifty thousand, five hundred and fifty five is 50\,555.

Idea summary

In a place value table, five-digit numbers start in the tens of thousands column and have a digit in each column down to the units.

## Order 5 digit numbers on a number line

Let's use a number line to order 5-digit numbers.

### Examples

#### Example 2

We want to work out which of three numbers is the largest.

a

Plot 41\,590, 41\,690, and 41\,490 on the number line below.

Worked Solution
Create a strategy

Find how much each space between tick marks represents.

Apply the idea

On the number lines the first two numbers are 41\,450 and 41\,500.

41\,500-41\,450=50, and there are 5 spaces between 41\,450 and 41\,500 which means that each space represents an increase of 10, since there are five lots of 10 in 50.

41\,490 is 4 tens more than 41\,450, so it should be 4 spaces to the right of 41\,450.

41\,590 is 4 tens more than 41\,550, so it should be 4 spaces to the right of 41\,550.

41\,690 is 4 tens more than 41\,650, so it should be 4 spaces to the right of 41\,650.

The numbers are plotted below:

b

Write the three numbers from smallest to largest.

Worked Solution
Create a strategy

Use the number line from part (a).

Remember that the smaller a number is, the further to the left on a number line it is.

Apply the idea

41\,490 was plotted furthest to the left which makes it the smallest.

Moving right 41\,590 was plotted next and then 41\,690.

So the numbers in order are:

41\,490, \,41\,590,\, 41\,690

Idea summary

The smaller a number is, the further to the left on a number line it is.

The larger a number is, the further to the right on a number line it is.

## Order 5 digit numbers using place value

This time we will see how to use a place value table to order 5-digit numbers.

### Examples

#### Example 3

Order these numbers from largest to smallest.

a

60\,679,70\,966,70\,669

Worked Solution
Create a strategy

Use a place value table and compare the digits from ten thousands.

Apply the idea

The numbers in a place value table is shown below:

We can see that 60\,679 has the smallest number of ten thousands so it is the smallest number.

70\,966 and 70\,699 have the same number of thousands.

70\,699 has less hundreds than 70\,966, so 70\,699 \lt 70\,966.

So the numbers from largest to smallest are:70\,966,70\,669,60\,679

b

95\,036,90\,536,95\,306

Worked Solution
Create a strategy

Use a place value table and compare the digits from ten thousands.

Apply the idea

The numbers in a place value table is shown below:

We can see that all the numbers have the same number of ten thousands.

90\,536 has the smallest number of thousands so it is the smallest number.

95\,036 and 95\,306 have the same number of thousands.

95\,036 has less hundreds than 95\,306, so 95\,036 \lt 95\,306.

So the numbers from largest to smallest are:95\,306,95\,036,90\,536

Idea summary

To determine the largest or smallest number in a pair, or set, of numbers, we can compare the furthermost left place value digits. If they are the same, we move to the right, one place at a time, until they are different.

We can also use the 'greater than' (\gt) or 'less than' (\lt) symbol to compare two numbers, remembering that the 'greater than' sign has the big part towards the larger number, and the 'less than' symbol has the small part towards the smaller number.

### Outcomes

#### VCMNA152

Recognise, represent and order numbers to at least tens of thousands

#### VCMNA153

Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems