We can order a group of numbers in either ascending or descending order by sorting the numbers into smaller groups that have the same highest place value; for example, 14 and 29.745 both have the highest place value of ten, which means that they will be in the same group.

We then order the different groups based on their highest place values; higher place value groups will be larger than smaller place value groups. We are then able to order the numbers in each group by comparing the numbers in the highest place value for each of the numbers in each group. If two numbers have the same number in their highest place value, we compare the number in the next place value to the right. We keep continuing this until there is a difference in the numbers in the same place values, thus meaning that we can say that one of the numbers is larger than the other. The best way to understand this is to go through an example.

We will do the opposite if we are asked to place the numbers into descending order.

We then order the different groups based on their highest place values; higher place value groups will be larger than smaller place value groups. We are then able to order the numbers in each group by comparing the numbers in the highest place value for each of the numbers in each group. If two numbers have the same number in their highest place value, we compare the number in the next place value to the right. We keep continuing this until there is a difference in the numbers in the same place values, thus meaning that we can say that one of the numbers is larger than the other. The best way to understand this is to go through an example.

We will do the opposite if we are asked to place the numbers into descending order.

**Example 1**

Place the following numbers in descending order:

The first step in ordering these numbers is to split the numbers into different sub groups based on the highest place value that the numbers have.

There are two numbers that have the highest place values in the hundred thousands; 155,324 and 143,798. There are three numbers that have the highest place value of the ten thousands; 72,253 and 87,399 and 34,154.

We now go onto comparing the numbers in the highest place value for each group. The question asks us to place the numbers in descending order. Therefore, we start ordering the group with the highest place value, which is the group with the highest place value of the hundred thousands. There are two numbers in this group; 155,324 and 143,798. The highest place value in this group is the hundred thousands. Both of the numbers have a 1 in this place value (the 1 means 100,000). This means that we must go onto the next place value and compare the numbers in this place value for the two numbers. The next place value is the ten thousands. 155,324 has a 5 in this place value, which means 50,000. 143,798 has a 4 in this place value, which means 40,000. 50,000 is greater than 40,000 and this means that 155,324 is a larger number than 143,798. We now have the largest and second largest numbers:

There are two numbers that have the highest place values in the hundred thousands; 155,324 and 143,798. There are three numbers that have the highest place value of the ten thousands; 72,253 and 87,399 and 34,154.

We now go onto comparing the numbers in the highest place value for each group. The question asks us to place the numbers in descending order. Therefore, we start ordering the group with the highest place value, which is the group with the highest place value of the hundred thousands. There are two numbers in this group; 155,324 and 143,798. The highest place value in this group is the hundred thousands. Both of the numbers have a 1 in this place value (the 1 means 100,000). This means that we must go onto the next place value and compare the numbers in this place value for the two numbers. The next place value is the ten thousands. 155,324 has a 5 in this place value, which means 50,000. 143,798 has a 4 in this place value, which means 40,000. 50,000 is greater than 40,000 and this means that 155,324 is a larger number than 143,798. We now have the largest and second largest numbers:

We are now onto the group that has the highest place value in the ten thousands. The numbers in this group are 72,253 and 87,399 and 34,154. To order these, we will be comparing numbers in the highest place value, which for these numbers is the ten thousands. 72,253 has a 7 in the ten thousands, which means 70,000. 87,399 has an 8, which means 80,000. And finally, 34,154 has a 3, which means 30,000. The largest number out of 7, 8 and 3 is 8 followed by 7, followed by 3. This means that the largest number in this group is 87,399, then 72,253 and finally 34,154.

Therefore, the numbers in descending order are:

Therefore, the numbers in descending order are:

The more you work with larger numbers, the more familiar you will be with them, which result in you being able to order them quicker. Also, you will get to the point where you are able to complete all of this working in your head.

**Example 2**

Place the numbers below is ascending order:

The first step in ordering these numbers is to split them into groups based on their highest place value. There are three different groups; the largest place value as the units (3.1), the largest place value as the tenths (0.8, 0.174 and 0.842) and the largest place value as the hundredths (0.0923).

We are ordering these numbers in ascending order, which means that we will be ordering them from the smallest to the largest. The smallest number will appear in the group that has the smallest highest place value, which is the group that has the largest place value as the hundredths. There is only one number in this group, and this means that the smallest number out of all of the 5 numbers is 0.0923.

We are ordering these numbers in ascending order, which means that we will be ordering them from the smallest to the largest. The smallest number will appear in the group that has the smallest highest place value, which is the group that has the largest place value as the hundredths. There is only one number in this group, and this means that the smallest number out of all of the 5 numbers is 0.0923.

We now move onto the next group that has the next smallest highest place value and this is the group that has the largest place value as the tenths. The numbers in this group are 0.8, 0.174 and 0.842. To place these numbers in ascending order, we compare the numbers in the highest place value; we are going to be comparing the numbers that are in the tenths place value. The numbers in the tenths value are 8 for 0.8, 1 for 0.174 and 8 for 0.842. The lowest number out of 8, 1 and 8 is 1, which means that the smallest number in this group is 0.174.

Both of the other numbers in this group have an 8 in their tenths place value. This means that we compare the numbers in the next place value to the right; we are going to be comparing the numbers in the hundredth place value. 0.8 can be written as 0.80 (all of the place values to the right of the 8 will be 0; we do not usually add the zeros because they do not add anything to the number). This means that 0.8 has a 0 in the hundredth place value and 0.842 has a 4 in the hundredth place value. 0 is smaller than 4, which means that 0.8 is smaller than 0.842.

The next group is the group that has the highest place value of the units. There is only one number in this group (3.1). This is the largest number out of all 5 of the numbers. The numbers in ascending order are shown below: