If a list of students is being given with the marks they have obtained in a certain examination and we have to find the ranking of students with respect to marks obtained. For this we need to arrange the given list from the highest marks obtained to the lowest marks obtained. Such an arrangement is known as descending order. The ordering of elements where each value will be higher than the next value in the order is called descending order. If the set of numbers have repetition of numbers then the descending order is known as non increasing order where the values can be decreasing or constant but they cannot increase.

## Descending Order Definition

The descending order arrangement can be defined as the ordering of a set of elements where the element with the largest value comes first and the element with the lowest value comes last. While we move down the ordered list of elements, each element will have a lesser value than the previous one. If there are numbers being repeated then each element will have the value less than or equal to the previous value. This will be known as non increasing ordering of elements.

Let us try to understand using an example.
44, 22, 8, 11, 56, 32

To write the above list of numbers in descending order we need to write the highest value first.
56

Then we need to write the rest of the values in decreasing order.
56, 44, 32, 22, 11, 8

If there are repeating elements in a given list such as,
7, 8, 2, 1, 2

Then the ordering from the highest value to the lowest value will be done as,
8, 7, 2, 2, 1

As we can see that the list is in non increasing order where each element is either less than or equal to the previous element.

## How to Write Numbers in Descending Order

Following steps should be followed in order to write a set of numbers in descending order:

1) Find the largest number in the set and write it at the first place.

2)
Exclude that number from the set.

3)
Find the largest number in new set and it at the next place.

4)
Repeat steps 2 and 3 till the set becomes empty.

Let us take a set of numbers, 11, 2, 14, 21, 5

Step 1: Write the largest number.
21

Step 2: Exclude 21 and the set becomes 11, 2, 14, 5

Step 3: Write the largest number at the next place,
21, 14

Now repeating steps 2 and 3,
21, 14, 11

Again repeating steps 2 and 3,
21, 14, 11, 5

Again repeating steps 2 and 3,
21, 14, 11, 5, 2

Now when we try to repeat step 2 we find that the set is null.

Hence, the descending order of elements are,
21, 14, 11, 5, 2

## Descending Order Examples

Example 1: Write the given set of elements in descending order.
211, 123, 256, 154
Solution:

Finding the largest element from the set and writing it.
256

Excluding 256 from the set and finding the largest element to write at the next place.
256, 211

Again excluding 211 from the given set and finding the largest element to fill the next space.
256, 211, 154

Excluding 211, the set has only one element left, that is, 123. Writing it at the next place.
256, 211, 154, 123

Excluding 123, the set becomes empty.

Hence, the elements in descending order will be written as,
256, 211, 154, 123
Example 2: Find the second smallest element from the given set of numbers.
65, 54, 78, 23, 29

Solution:
To find the second smallest number, we can write the elements in the descending order and the second last element in the list will be the second smallest element.

Step 1: Write the largest element.
78

Step 2: Exclude 78 from the set and the set becomes 65, 54, 23, 29. Write the largest element of this set at the next place.
78, 65

Step 3: Exclude 65 from the set and the set becomes 54, 23, 29. Write the largest element of this set at the next place.
78, 65, 54

Step 4: Exclude 54 from the set and the set becomes 23, 29. Write the largest number at the next place.
78, 65, 54, 29

Step 5: Exclude 29 and the set becomes 23. Write the largest element at the next place.
78, 65, 54, 29, 23

Step 6: Exclude 23 and the set becomes empty.

Hence, the given numbers in descending order are:
78, 65, 54, 29, 23

The second last element in the list is 29. It implies that the second smallest element is 29.