Ascending Order

Ascending order refers to the arrangement of numbers or other items in an increasing order, that means from smallest to largest. Numbers that we see on a number line from left to right is an example of ascending order. We usually represent it by putting commas between numbers or by using 'less than symbol (<)' between numbers. For example, 1, 2, 3, 4, 5 or 1<2<3<4<5 are in ascending order.

Have you ever come across situations where you have so many important folders/files/documents that may be useful to you, but because they are so many in number, you can't find the correct one? Well, most of such problems can be solved if you arrange them in some particular pattern or order. Arranging things in ascending order is one way to collect and represent data.

Table of Contents

What is Ascending Order?

Ascending means increasing. So when any quantity/map/list has its values from smallest to largest, we say that it is an ascending quantity/map/list. This increase can be in any form such as alpabets, weights, heights, and time.

For example, we say, "The rocket is ascending into the sky." Here, it means that the rocket's distance from the ground after lift-off is constantly ascending as it orbits into space. This was a general idea for the word "ascending." Now, let us try to narrow down our knowledge to "ascending order."

Ascending Order: Definition

The arrangement of data from the smallest to the largest value is known as Ascending order. It is also known as increasing order. For example, consider the following numbers: [6,2,8,4,0]. Now, we try to arrange them in an increasing form. Thus, we get,

Numbers in ascending order

Hence, the numbers arranged in ascending order are given by [0, 2, 4, 6, 8 ]

Ascending Order Symbol

To represent a given set of numbers in ascending order, we can either put commas ',' or we can use 'less than symbol (<)'. The most common way to represent numbers in ascending order is by putting less than symbol in between, which shows that the number at the left is smaller in value than the number at the right side of the symbol.

Rules of Ascending Order

While arranging a given set of numbers in ascending order, there are few rules that we need to keep in our minds. Those rules are listed below:

  • The first value is always the smallest.
  • The values should always be in order from smallest to largest.
  • The last value is always the largest.

For example, in the ascending arrangement: [49, 54, 89, 623, 810]

  • The number 49 is the smallest, hence the first one in the list.
  • The number 810 is the largest, hence the last one in the list.

Ascending Order of Negative Numbers

Ascending order of negative numbers means to arrange the given negative numbers from smallest to largest values. It is very important to learn it as in the case of negative numbers the absolute values of smaller numbers are greater than the absolute values of larger numbers, so many times people find it confusing. 

With negative numbers, the highest number with the negative sign has the least value. So, if you have to arrange -34, -56, -4 into ascending order, then it is arranged in the following order: 

-56 < -34 < -4

-4 is the largest number and -56 is the smallest number out of the given three numbers.

Look at the image given below to understand ascending order and descending order of numbers on a number line.

Numbers in ascending order

Ascending Order of Fractions

Ascending order of fractions means to arrange the given fractions in increasing order. In the case of fractions, there are two ways to arrange them into increasing order and those are listed below:

  • By converting fractions to decimals
  • By converting given fractions into like fractions

We can convert fractions to decimals by dividing the numerator with the denominator, and then we can arrange those decimals into ascending order by looking at the whole number part and the decimal part place values. And with the second method, we convert the denominators of all the given fractions into the LCM of the denominators by multiplying the same number to numerator and denominator. Then we compare the values in the numerator of the fractions so obtained and arrange them in increasing order.

Example: Arrange the following fractions in ascending order: 1/2, 2/5, 5/6, 3/5

Solution: If we convert these fractions into their decimal equivalents one by one, we get, 

              1/2= 0.5

              2/5= 0.4

              5/6= 0.83

              3/5= 0.6

Now, all these decimals have 0 in the whole number part, so we have to look at the digit at the tenth place to arrange these numbers in ascending order.

0.4 < 0.5 < 0.6 < 0.83

∴ 2/5 < 1/2 < 3/5 < 5/6.

No, let us look at the solution of the same example by using the like fractions method.

Given fractions are 1/2, 2/5, 5/6, 3/5.

LCM of {2, 5, 6}= 30

1/2 × 15/15= 15/30

2/5 × 6/6= 12/30

5/6 × 5/5= 25/30

3/5 × 6/6= 18/30

Now, we can easily compare the numerators of these fractions, i.e 12<15<18<25.

12/30 < 15/30 < 18/30 < 25/30

∴ 2/5 < 1/2 < 3/5 < 5/6.

Important Topics

Given below is the list of topics that are closely connected to ascending order. These topics will also give you a glimpse of how such concepts are covered in Cuemath.

FAQs on Ascending Order

How do you Arrange in Ascending Order?

Ascending order is an arrangement from smallest to largest value. For example, {4, 7,10,13} are numbers arranged in ascending order. While arranging numbers in ascending order, we write the smallest value first and then we move forward towards the largest value.

What is the Ascending Order Sign?

The symbol used to arrange numbers in ascending order is '<'. Therefore, less than symbol or < is the ascending order sign.

What is the Difference Between Ascending and Descending Order?

When the numbers are arranged in smallest to largest format, they are said to be in ascending order. On the other hand, when the numbers are arranged in largest to smallest format, they are said to be in descending order.

How to Arrange Decimals in Ascending Order?

Decimals are arranged in ascending 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 digit in the whole number part is the same for two or more numbers, then we look at the digit at the tenth place of the number (i.e 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 hundredth place and so on. This is how we arrange decimals in ascending or increasing order. For example, 1.3 < 1.35 < 1.356 < 2.3 < 4.08.

How to Arrange Integers in Ascending Order?

Integers are numbers without fractional or decimal part. They include whole numbers and their negatives on the other side of the number line. On a number line, if we move towards right, then we get integers written in ascending order. For example, -5 < -4 < -3 < -2 < -1 < 0 < 1 < 2 < 3 < 4 < 5.

Solved Examples

Example 1:

In a school, Ms. Janet recorded the heights of five students in her class. The heights are: {3 feet 7 inches, 3 feet 4 inches, 3 feet 2 inches, 4 feet 2 inches, 3 feet 8 inches}. Arrange the heights in ascending order.


To arrange the heights in ascending order, we start with the shortest student. The heights in ascending order are:

{3 feet 2 inches < 3 feet 4 inches < 3 feet 7 inches < 3 feet 8 inches < 4 feet 2 inches}

Example 2:

Harry counted the number of windows in each house of his neighborhood. He made a list as follows: {15, 7, 13, 6, 11, 17, 10}. Arrange the list in ascending order.


The number of windows in ascending order is: {6 < 7 < 10 < 11 < 13 < 15 < 17}.

Practice Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result. 

More Important Topics