Ascending order refers to arranging items in a sequence where the smallest, first, or earliest element appears at the top of the list. When sorting numbers or amounts, this means arranging them from smallest to largest, with lower numbers or amounts listed first. Similarly, when sorting letters or words, items are arranged alphabetically from A to Z.

In simple words, 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. In this article, we will study how to arrange numbers in ascending order, with the help of solved examples.

Ascending Order Meaning

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 numbers in 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

What is Increasing Order?

Increasing order is a synonym of ascending order. It is a way of arranging items, values, or data from the smallest to the largest. This arrangement begins with the lowest value and progresses to the highest value.

It is commonly used for sorting numbers, organizing data in tables, and arranging items based on their magnitude.

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.

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

Negative Numbers in Ascending Order

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

• 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

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

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.

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.