**Online Math Classes > Math Concepts > Number Sense > Ordering Numbers**

You are given a set of blocks with numbers printed on them and asked to place them in a certain order. What is the best way to arrange them? You look for a way to arrange things in a pattern. This procedure of arranging numbers is referred to as **ordering numbers**.

Ordering numbers is the process of arranging numbers from the greatest to the least or from the least to the greatest.

**Illustration 1
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Two friends Sarah and Rebecca were playing a game of arranging numbers. They have a set of numbers given as shown below:

While arranging numbers one should look for the greatest or the least number, in the given set of numbers, to start with.

Sarah decided to arrange them in the ascending order. She should identify the least number from the given set of numbers. Here, 1 is the least number. The immediate smallest number available in the list after 1 is 2. Following the same process, she arranged the numbers from the least to the greatest as shown below:

Rebecca decided to arrange them in the descending order. She should identify the greatest number from the given set. Here, 10 is the greatest number. The immediate largest number available in the list after 10 is 9. Following the same process, she arranged the numbers from the greatest to the least as shown below:

**Illustration 2**

Mr. Kevin was the proud owner of four dogs. As seen, each dog has been assigned a tag number for identification.

Kevin has built four shelters for dogs. He wants to allocate each shelter to one dog. The dog houses are numbered 1 to 4 in the ascending order as pictured.

If each dog is allocated a house in the ascending order of their tags, then which dog gets into the first shelter?

Recall the definition of ascending order of numbers. Ascending order involves arranging numbers in the increasing order starting from the least to the greatest. Here, the least number in the given set of tag numbers is 5. Hence, a dog with tag 5 will be in first place and dogs with tags 6, 7 and 8 will be in houses numbered 2,3 and 4 respectively. The arrangement is shown below.

If each dog is allocated a house in the descending order of their tags, then which dog gets into the first shelter?

Recall the definition of descending order of numbers. Descending order involves arranging numbers in the decreasing order starting from the greatest to the least. Here, the greatest number in the given set of tag numbers is 8. Hence, a dog with tag 8 will be in first place and dogs with tags 7, 6 and 5 will be in houses numbered 2, 3 and 4 respectively. The arrangement is shown below.

**Can you do it yourself?**

Arrange the numbers in the ascending and the descending order.

**Solution:**

## Ordering numbers using place value

You are familiar with ordering single digit numbers. Assume that there is a set of numbers having more than one digit. Let us now learn how to arrange them in an order.

We use the concept of place values to recognize the greater or the smaller numbers. Let us use some examples and understand the concept.

**Example 1: Arrange the following numbers in the ascending order.
56, 78, 59, 47, 93**

**Solution: **

Given numbers: 56, 78, 59, 47, 93

Every number in the above set consists of two digits, so consider the tens place of each number. Identify the least valued number in tens place. If two numbers have the same number in the tens place, then check for the least number in ones place. Here, the least number among the given numbers is 47. The number 47 will be in the first position.

To identify the number for the second position, look for the next number in the ascending order. Here, 5 is the number greater than 4. But, there are two numbers having 5 in the tens place. Look for the greater number in the ones place, 6 < 9. So, 56 will be in the second position, followed by 59.
Since, 7 < 9, 78 will be in the fourth position and 93 will be in the last. The arrangement of numbers is 47, 56, 59, 78, 93.
One should follow the same procedure to arrange the list of numbers in ascending or descending orders.

**Example 2: Arrange the following numbers in the descending order.
247, 375, 452, 294**

**Solution:**

Given numbers: 247, 375, 452, 294

In all four numbers, hundreds place is the greatest place value. So look the digits at hundreds place and compare them. Here, 4 > 3. Hence, 452 will be in the first position, followed by 375, i.e., 452 > 375.

247 and 294 have the digit 2 in the hundreds place. But, the digits in tens place are different, 9 > 4. Therefore, 294 will be in the third position, followed by 247.

Thus, the number can be arranged as 452, 375, 294, 247.

**Example 3: Arrange the following numbers in the descending order.
786, 2503, 125, 3671, 76**

**Solution:**

Given numbers: 786, 2503, 125, 3671, 76

In this list of numbers, thousands place is the greatest place value. So, to compare the numbers, look at the thousands place. Among 3671 and 2503, 3 > 2; thus 3671 will be in the first position followed by 2503.

The next greatest place value is hundreds place. Among 786 and 125, 7 > 1; thus 786 will be in the third position followed by 125 in the fourth position.

The number 76 is the least among all the numbers in the list.

Thus, the numbers can be arranged as 3671, 2503, 786, 125, 76.

Similarly, the numbers can be arranged in ascending order as 76, 125, 786, 2503, 3671.

When the numbers are given, one can follow the same procedure to identify the position of the number based on its place value and arrange them in the ascending or descending orders.

## Math Facts

Know more about other concepts of Number Sense on Counting, Cardinality, Comparing Numbers, Ordinal Numbers and Odd and Even Numbers