Ascending Order: Meaning and Examples | Increasing Order

Ascending Order is the arrangement of objects in a sequence such that the next element is always greater than the previous one. It is also called increasing order.

Let’s learn how to arrange numbers in ascending order, with the help of solved examples.

Meaning of Ascending Order

Ascending Order means numbers are arranged in increasing order, from the smallest to the largest. The first number in ascending sequence is the lowest, while the last number is the biggest.

We make sure that every number in the series is bigger than or equal to the one before it while sorting a set of number in the increasing order.

Ascending Order Symbol

The less than sign, “<” stands for increasing order. For instance,

1 < 2 < 3 < 4 < 5 < 6 < 7 < 8 < 9

Ascending Order Examples

Some of the examples of numbers arranged in increasing order are as follows,

1. 2<3<4<5
2. 100<101<102<103
3. 253<350<380<600
4. 1000<2001<2056<2100

Ascending Order on Number Line

To illustrate ascending order on a number line, let us imagine a horizontal line with a point at the origin (0). The numbers increase in size as you move toward the right of the line.

For example, Let’s take the numbers 1, 3, -2, 0, and 4.

The smallest number, -2, would go in the leftmost place in the increasing order. We would proceed in this manner after placing 0 to the right of -1, 1 to the right of 0, 3 to the right of 1, and then 4 to the right of 3.

The resulting arrangement on the number line would look like this:

-2 < 0 < 1 < 3 < 4

The number line shown above represents this sequence.

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• Numbers
• Number Line

How to Arrange Numbers in Increasing Order?

In order to arrange the numbers in ascending order, we must first compare the values before doing so.

Here, we may arrange several numbers, including:

• Integers
• Negative Numbers
• Fractions
• Decimals

Integers in Ascending Order

The integers are the number that are both positive and negative and they also include zero. The integers are easily arranged in ascending order by following the basic rule,

• All the negative integers are less than Zero(0) and all the positive numbers are greater than Zero(0).
• All the positive numbers are greater than all the negative numbers.
• In case of the positive number, they are compared normally and arranged in increasing order.
• In case of the negative number they are arranged in the descending order of their absolute values. Then the negative sign is applied and the resulting sequence is in ascending order.

Let us arrange these numbers in ascending order : -7, -9, -23, 11, 5, 0

-23 < -9 < -7 < 0 < 5 < 11

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• Integers

Negative Numbers in Ascending Order

Negative numbers are arranged in ascending order by simply following the rule discussed below,

• The absolute values of all the negative numbers are taken and then they are arranged in the descending order of their values.
• The negative sign is put and then the numbers are arranged in the ascending order.

For example, arrange -11, -45, -32, -23 in ascending order :

-45 < -32 < -23 < -11

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• Negative Numbers
• Absolute Values

Fractions in Ascending Order

Fractions are easily arranged in increasing order by making all the fractions as like fractions and then arranging them in ascending order in the order of their numerator.

For example, let us arrange 1/6, 2/3, 5/12, 7/4 in ascending order.

For changing the given fraction into like fractions we must make the denominators of the fractions equal.

LCM of 6, 3, 12, 4 = 12

• 1/6 = 2/12
• 2/3 = 8/12
• 5/12 = 5/12
• 7/4 = 21/12

Arranging them in the increasing order we get :

2/12 < 5/12 < 8/12 < 21/12

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• Fractions

Decimals in Ascending Order

Decimals in ascending order are arranged by following the steps discussed below,

Step 1 :In comparing 7.8 and 8.1 we only compare the whole number part, as 7 < 8, so

7.8 < 8.1

Step 2 : If the whole number part is equal then we compare the decimal part one by one as,

7.890 and 7.891 here,

7.890 < 7.891.

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• Decimal Number System

Ascending Order and Descending Order

Descending order is the opposite of ascending order.

Let’s discuss the differences between the ascending order and the descending order.

Increasing Order	Decreasing Order
Difference between Increasing and Decreasing Order
In ascending order, the number are arranged in order from smaller to larger.	In descending order, the numbers are arranged in order from larger to smaller.
The two consecutive numbers are in ascending order. The second number is always greater than the first number.	The two consecutive numbers are in descending order. The second number is always less than the first number.
It is represented using “<” the symbol.	It is represented using “>” the symbol.
For example, in ascending order, the numbers are arranged as,  2 < 4 < 6 < 8	For example, in ascending order, the numbers are arranged as,  8 > 6 > 4 > 2

Solved Questions on Increasing Order

Let’s solve some questions on the concepts of increasing order.

1. Arrange the following fractions in ascending order, 1/2, 2/3, 3/4, and 4/5

Solution:

The fraction as discussed above is arranged in ascending order by making all the fraction to be like fractions.

Given fractions, 1/2, 2/3, 3/4, and 4/5

LCM of 2, 3, 4, and 5 = 60

• 1/2 = 30/60
• 2/3 = 40/60
• 3/4 = 45/60
• 4/5 = 48/60

Now for the like fractions, the ascending order is found by arranging the numerator in the ascending order.

30 < 40 < 45 < 48, thus

30/60 < 40/60 < 45/60 < 48/60

The required fractions in ascending order are arranged as, 1/2 < 2/3 < 3/4 < 4/5

2. Arrange the following decimals in ascending order, 1.3, 4.5, 5.6, and 2.8

Solution:

In decimals, the numbers are arranged in ascending order by comparing their whole part, i.e.

1 < 2 < 4 < 5, so

The required decimals in ascending order are 1.3 < 2.8 < 4.5 < 5.6

3. Arrange the following integers in ascending order, -1, -4, 5, and 2

Solution:

The integers are arranged in ascending order as negative integers are greater than the positive integers so,

The required integers in the ascending order are -4 < -1 < 2 < 5.

4. Arrange the following negative numbers in ascending order, -2, -45, -23, and -17

Solution:

In the case of the negative numbers, the modulus part is compared and the modules part of the negative number in the descending order is equal to the ascending order of the negative numbers.

The required negative numbers in ascending order are, -45 < -23 < -17 < -2

Increasing Order- FAQs

1. What is Ascending and Descending Order?

Ascending order is the method of arranging values in increasing , where each element is greater than or equal to the preceding element. Descending Order, on the other hand is the arrangement of objects in a sequence such that the next element is always amller than the previous one

2. How to Arrange Numbers in Increasing Order?

To arrange numbers in ascending order, compare the numbers in pairs and swap their positions if necessary, starting from the beginning of the set. Repeat this process until the entire set is sorted. The result is a sequence from the smallest to the largest number.

3. How to Arrange Fractions in Ascending Order?

To arrange fractions in ascending order, change the fraction into like fractions (i.e. fractions with equal denominator) then compare the numerator of the fractions and arranged them in ascending order of the numerator.

4. How to Arrange Negative Numbers in Increasing Order?

To arrange negative numbers in the increasing order first take the absolute values of the given negative number and then arrange them in the descending number and add a negative sign to get the ascending order of the negative numbers.

5. How to Arrange Negative Numbers in Ascending Order?

We can arrange negative numbers in ascending order by comparing their absolute values. Smaller values come first, and for numbers with the same value, the one with the greater negative value goes first.