Descending Order

Descending order is a way to arrange numbers from largest to smallest. When we arrange things in order, from a higher value to a lower value, it is known as the descending order or the decreasing order. Let us learn more about it in this article.

Arranging in descending order means arranging any data like numbers, alphabets, quantities, lengths, etc., from the highest to the lowest. In other words, when we arrange things in an order from a higher value to a lower value, they are said to be in descending order. Numbers like whole numbers, natural numbers, integers, fractions, decimals can be arranged in descending order. For example, let us arrange {7,3,9,2} in decreasing order. We will start with the largest number and move towards the smaller numbers one by one. These numbers, when arranged in descending order, are written as 9 > 7 > 3 > 2, or 9, 7, 3, 2.

Backward counting involves arranging numbers in descending order and forward counting involves arranging the numbers in ascending order. However, a certain number of rules need to be followed while arranging any items in descending order. The rules are as follows:

1. The first number should always be the largest number.
2. The numbers should always be in order from the largest to the smallest.
3. The last number should always be the smallest among the given numbers.

Descending Order Symbol

The symbol used to write numbers in descending order is the greater than symbol, ">". The open end will face the larger number while the pointed end will face the smaller number. For example, let us arrange the numbers 2, 4, 6, 1, 5, and 7 in descending order. When we arrange these numbers in descending order, the symbol is placed in the following way, where the open end faces towards the bigger number: 7 > 6 > 5 > 4 > 2 > 1. In many places, you might find that a comma is used for the arrangement of numbers in descending order. For example, 7, 6, 5, 4, 2, 1. This is also a correct way of representing the order of numbers from highest to lowest.

The opposite of descending order is the ascending order, which means to arrange items/numbers from smallest to largest. The first four natural numbers in descending order is 4 > 3 > 2 > 1, and the same set of numbers in ascending order is 1 < 2 < 3 < 4.

Now, let us learn the difference between ascending order and descending order in the section below.

Difference between Ascending and Descending Order

The difference between ascending and descending order is clearly shown in the table given below:

To arrange fractions in descending order, we need to know the concept of comparing fractions. In order to arrange like fractions in decreasing order, compare their numerators and arrange them from largest to smallest values. For example, 2/3, 1/3, and 5/3 can be arranged in descending order as 5/3 > 2/3 > 1/3, as 5 > 2 > 1. On the order hand, to arrange fractions with the common numerator and different denominators, we observe the numbers written in the denominators and arrange them from smallest to largest. It is because, for such fractions, the value of a fraction with a smaller denominator is greater than the value of a fraction with a larger denominator. For example, 1/2, 1/3, and 1/5 can be arranged in descending order as 1/2 > 1/3 > 1/5.

To arrange unlike fractions in descending order, the first step is to convert them to like fractions and then compare their numerators. The fraction with the largest numerator is the highest and the fraction with the smallest numerator is the smallest among all the given like fractions.

Decimals are arranged in descending order by looking at the digits from left to right according to the place value of decimal numbers. First, we look at the whole number part. If the digits in the whole number part are the same for two or more numbers, then we look at the digit at the tenths place of the number (i.e., the first digit to the right of the decimal point). If the digit in the tenths place is also the same, then we look at the digit at the hundredths place and so on. This is how we arrange decimals in descending or decreasing order. For example, 5.9 > 3.67 > 2.45 > 2.41 > 2.07 > 1.99 shows the arrangement of decimal numbers in descending order. Refer to the article comparing decimals to learn more.

Related Topics

Check these interesting articles related to descending order in math.

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What is Descending Order?

Descending order in math is defined as the arrangement of items/numbers from highest to lowest. It moves in a downward direction as the numbers keep on decreasing. The descending order is also known as decreasing order.

What is Ascending Order and Descending Order?

Ascending and descending order are opposite of each other. If we arrange numbers from smallest to largest, it means we arrange them in ascending order. On the other hand, if we arrange numbers from largest to smallest, it means we arrange them in descending order.

How do you Arrange in Descending Order?

Descending order is an arrangement of numbers from the largest to the smallest. We start arranging the numbers by placing the largest number first and moving towards the smaller numbers one by one. For example, if we arrange the numbers 63, 99, 10, 87, 35 in descending order, we write them as 99, 87, 63, 35,10.

What is the Descending Order Sign?

The symbol used to arrange numbers in descending order is ">". When we arrange numbers in descending order, the symbol is placed in a way such that the open end faces towards the bigger number. For example, here is a list of numbers arranged in descending order, 37 > 26 > 15 > 4 > 3 > 2 > 1.

What is the Difference Between Ascending And Descending Order?

Ascending order is the arrangement of numbers from the smallest to the largest. For example, the following numbers are in ascending order: 3, 15, 28, 49. Descending order is an arrangement of numbers from the largest to the smallest. For example, the numbers 45, 32, 26, 12 are arranged in descending order.

What is Descending Order in Fractions?

Descending order of fractions is the arrangement of fractions from the highest value to the lowest. Like fractions can be arranged in descending order by looking at their numerators from the highest to lowest. And unlike fractions can first be converted to like fractions followed by arranging them as per their numerators from largest to smallest.

How to Arrange Decimals in Descending Order?

Decimals are arranged in descending order by looking at the digits from left to right. First, we compare the whole number part and arrange it in descending order. Now, for the ones which have the same whole number part, we need to compare the decimal part. We do this according to the place value of decimal numbers. We know that for the numbers 2.45 and 2.41, the non-decimal part is the same, i.e 2. So, we compare the decimal part. After comparing 0.45 and 0.41, we can see that 0.45 is the higher one. Hence, 2.45 is greater than 2.41. For example, 7.09 > 2.67 > 0.4 shows the arrangement of decimal numbers in descending order.

How to Arrange Fractions in Ascending and Descending Order?

Like fractions can be arranged in descending order by looking at their numerators. For example, 4/7, 9/7, and 2/7 can be arranged as 9/7 > 4/7 > 2/7. It is because 9 is greater than 4 which is greater than 2. Unlike fractions need to be converted to like fractions first and then we can use the same method to arrange them in descending order. For unlike fractions with the common numerator and different denominators, the fraction with the smallest denominator is the greatest. For example, 2/3 > 2/4 > 2/5.

Is Descending Order Greatest to Least?

Yes. When we arrange things in order, from the greatest value to the lowest value, it is known as the descending order or the decreasing order. In this arrangement, we place the greatest value first and move towards the smaller numbers one by one. For example, the numbers: 27, 14, 7, 3 are arranged in descending order.