Ascending Order

Ascending order is a method of arranging numbers from smallest to largest. We can also say arranging the numbers in increasing order. 

For example, a set of natural numbers are in ascending order, such as 1, 2, 3, 4, 5, 6, 7, 8… and so on. The inverse of increasing order is decreasing order or descending order. 

Learn the ascending order definition, symbol/sign, examples, representation on a number line, ascending order of fractions, solved problems, etc., in this article.

What do you mean by Ascending Order?

In Mathematics, the process of arranging the numbers from smallest to largest is called ascending order. The numbers are arranged from left to right in increasing order. 

The other terms used for ascending order are:

  • Lowest to highest
  • Bottom to Top

Ascending Order

Ascending order symbol

Ascending order is represented by the less than symbol ‘<‘. 

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

The symbol represents that the succeeding number is greater than the preceding number in the arrangement. 

The sign of ascending order represents numbers from lowest to highest, which is opposite to the concept of descending Order, where numbers are arranged from largest to smallest.

Examples of Ascending Order

  • 1 <  2 < 3
  • 10 < 11 < 12 < 13
  • 100 < 1000 < 10000
  • -10 < -9 < -8 < -7

Ascending Order on Number Line

The concept of ascending order is been introduced in primary classes for students of Class 1. With the help of the number line, students can easily understand the arrangement of numbers in increasing order. 

In the above number lines numbers from -6 to 6 are arranged in ascending order. It states that numbers on the left side of 0 are smaller than the numbers on the right side of 0. As we go from left to right on the number line the value of numbers increases.

How to Arrange Numbers in Ascending Order?

To arrange the numbers in ascending order, first, we need to compare the values and then order them in ascending order. 

We can arrange here different numbers such as:

  • Integers
  • Negative numbers
  • Fractions

Integers

As we know integers are numbers that can be negative, positive or zero. But they are not fractions. Let us learn how to arrange positive integers in ascending order. 

  • Firstly compare the number of digits in each number
  • The number with lesser digits is the smallest number
  • The number with the largest digits is the largest number
  • If the number of digits is the same, then compare the left-most digits of the numbers
  • Compare the numbers in the same manner and arrange them all from smallest to largest.
Example: 2 < 4 < 12 < 23 < 451 < 541

Negative Numbers

Arranging negative numbers can be a little challenging for the students at the beginning. But once they have understood the logic, it will be very easy for them to arrange the numbers in ascending order.

If a bigger number is having a negative sign, then it becomes the smallest value. For example, 3 is greater than 2, but -3 is smaller than 2.

Similarly, a two-digit negative number is smaller than a single-digit negative number. 

-43 < -8

-50 < -25 < -10 < -1 

Fractions

There are two methods involved in finding the ascending order of the fractional numbers. Both the method will give the same solution

Method 1:

  • Step 1: For a given series of fractions, first convert it into decimal numbers.
  • Step 2: Find the increasing order of the decimal numbers.
  • Step 3: Finally, replace the decimal values with the respective fractional numbers.

Method 2 :

  • Step 1: Find the L.C.M of the denominators.
  • Step 2: Divide the L.C.M value by the denominator of the fraction.
  • Step 3: Multiply both the numerator and denominator of the fraction with the resultant value of step 2.
  • Step 4: As a result of step 2 and step 3, compare the like fractions.
  • Step 5: Since the denominators are the same, compare the numerator values of like fractions.
  • Step 6: Finally, arrange the fractions in increasing order with its respective fractions given in the problem.

Ascending order of Alphabets

Same as numbers you can also arrange alphabets in ascending order and descending orders. For example : a < b < c < d < e < f < g < h < i < j <  k < l < m < n < o < p < q < r < s < t < u < v < w < x < y < z (For small alphabets). 

You can reverse the order of the alphabets in the case of descending order.

Ascending Order and Descending Order

Descending order is the contradiction of ascending order. That means it is the opposite process of writing the numbers in increasing order. Therefore, it can be mentioned as a decreasing order. In the case of descending order, for a given set of numbers, the highest valued number is written first, and the lowest valued number is written at last. It is denoted by the symbol ‘>’.

Ascending Order Descending Order
Numbers are arranged in increasing order Numbers are arranged in decreasing order
Smallest to largest  Largest to smallest
It is represented by less than symbol: ‘<’ It is represented by greater than symbol: ‘>’
Example: 3<6<7<9<10 Example: 10>9>7>6>3

Solved Examples

Question 1: Arrange the following numbers in increasing order :

63 , 72 , 42 , 26 ,34 and 102

Solution: Given , 63 , 72 , 42 , 26 ,34 and 102

63 = 6 x 6 x 6 = 216

72= 7 x 7 =49

42 = 4 x 4 = 16

26 =2 x 2 x 2 x 2 x 2 x 2 = 64

34 = 3 x 3 x 3 x 3 = 81

102 = 10 x 10 = 100

Therefore, the increasing order of the numbers are 16, 49, 64, 81, 100 and 216 and will be represented as  : 42 < 72 < 26 < 34 < 102 < 63

Question 2: Arrange the numbers 34, 10, 6, 4, 45, 25 in ascending order.

Solution: The increasing order of the numbers are 4, 6, 10, 25, 34 and 45

Question 3: Write these numbers in ascending order: 8, 10, 92, 1, 27.

Solution: The following is the increasing order of the given numbers:

1 < 8 < 10 < 27 < 92

Question 4: Find the increasing order of the following fractions: 8/6, 2/3, 10/12 and 9/6.

Solution:

Given series: 8/6, 2/3, 10/12 and 9/6.

Step 1: Converting fractions into decimals

8/6 = 1.33

2/3 = 0.67

10/12 = 0.83

9/6 = 1.5

Step 2: Arranging the increasing order of the decimal values

0.67 < 0.83 < 1.33 < 1.5

Step 3 : Replacing the decimal values with fraction values

2/3 < 10/12 < 8/6 < 9/6

Therefore, the increasing order of the given fractions are 2/3, 10/12, 8/6 and 9/6.

Question 5: Write 3, 7, 8, 2, 10, 28, 15 in descending order.

Solution: 28 > 15 > 10 > 8 > 7 > 3 > 2 is the descending order of the given set of numbers.

Practice Problems on Ascending Order

These problems are the worksheet for students to practice more in ascending order.

    1. Arrange in ascending order: 2, 1, 7, 3, 4.
    2. Write the numbers in increasing order: 90, 34, 92, 1, 35.
    3. Write the numbers in ascending order using the symbol: 80, 1, 12, 10, 72.
    4. Rearrange the numbers in increasing order: 18, 11, 67, 19, 07.
    5. Write the numbers in increasing order: 7, 15, 90, 81, 56.

Download BYJU’S – The Learning App to get information about the Maths-related articles and worked problems.

Frequently Asked Questions – FAQs

What is the ascending order and descending order?

When the numbers are written in increasing order, smallest to largest value, then it is said to be ascending, for example, 3<5<7<9<11<13 When the numbers are written in decreasing order, i.e. largest to smallest value, then it is said to be descending order. For example, 13>11>9>7>5>3

How can we arrange the numbers in increasing order?

Suppose a set of values are given: 23, 11, 15, 9, 55, 43.
By arranging them in ascending order, we have to figure the smallest value first, which is 9.
9
Now the number greater than 9 here is 11. Therefore,
9<11
It indicates that 11 is greater than 9. In the same way, we can arrange all the numbers as;
9<11<15<23<43<55

What is ascending order in A to Z?

Ascending order means going up from small value to high value and text from A to Z. Descending order means arranging the numbers from largest to smallest and text from Z to A.
When the names are arranged for a list, then it is usually arranged in A to Z order, alphabetically.

How to arrange negative numbers in ascending order?

To arrange negative numbers, we should always remember that the highest number with a minus sign (-) or negative symbol, is the smallest value.For example, -3, -8, -10, -4, -9 are the integers. Then on arranging them in increasing order, we get;
-10, -9, -8, -4, -3
Hence, -10 is the smallest value here, and -3 is the largest one.

What is the sign of ascending and descending orders?

Ascending order is represented by < (less than) symbol, whereas descending order is represented by > (greater than) symbol.

Quiz on Ascending Order

4 Comments

  1. APARNA RAJIV MENON

    Arrange the following fractions in ascending order.

    5/6, 8/9, 2/3

    1. 2/3, 5/6, 8/9

  2. Arrange these numbers in ascending order 45,99,9,81,27,63,18,36,90,54,72

    1. Ascending order = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99

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