Ascending Order

Ascending order refers to the arrangement of numbers in increasing order, i.e., from smallest to largest. The word 'ascending' means climbing high. For example, a rocket ascends into the sky. Learning the concepts of ascending and descending order holds great importance in developing foundational skills. By understanding the concept of ascending order, you can easily attain number sense that further builds a solid foundation for core math topics like place value, data representation, pattern recognition, logical reasoning, etc. Along with math skills, learning ascending order also enables us to tackle many real-life problems, like comparing prices, arranging things, etc. It also helps us to sort things better by grouping and organising them based on their size, height, weight, quantity, and so on. 

Table of Content

• What is Ascending Order?
• Symbols Used for Ascending Order
• Representation Using Number Line
• How to Arrange in Ascending Order?
• Application of Ascending Order Concept in Real Life
• Samples Problems
• Frequently Asked Questions

What is Ascending Order?

In mathematics, ascending order is defined as a way of arranging values from smallest to largest. Consider the following numbers: 8, 2, 7 & 10. To arrange these numbers in ascending order, we place the smallest number first, followed by the second, third, and fourth largest numbers. That is, 2 < 7 < 8 < 10.

The above image shows the ascending order of animals based on their size.

Symbols Used for Ascending Order

We use the comparison operator 'less than' (<) to indicate the relationship between two values arranged in ascending order. For example, for a given set of natural numbers we can represent the ascending order using the (<) symbol as 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8… and so on. 

The less than symbol (<) is used to denote the increasing order. The inverse method of increasing order is descending order, where the numbers are arranged in decreasing order of values.

Representation Using Number Line

Kids are introduced to the concept of ascending order in primary grades. The pictorial representation of ascending order on a number line helps kids to quickly grasp this concept.

Arranging numbers in increasing order on a number line is easy for kids to learn. For example, in the above number line picture, the numbers are arranged in ascending order from 1 to 10. As we go from left to right on the number line, the value of the numbers increases.

How to Arrange in Ascending Order?

Ascending order is the process of arranging and writing numbers in a list from the smallest to the largest. The step-by-step explanation of the process of arranging in ascending order is mentioned below:

1: Check the numbers to compare place values: Carefully compare the place values of numbers with digits in the ones, tens, and hundreds places. For example, to compare the numbers 12, 7, and 25, compare all the digits in the ones and tens places.

2: Identify the Smallest Number: After comparing, encircle the number with the lowest value in the ones place; this number will come first in ascending order. I.e., 7 is the smallest and will come first in order.

3: The next step is to find the second smallest number. After placing the smallest, look for the next bigger number. Repeat until all numbers are arranged.

Therefore, the order of the numbers given in the above example is 7 < 12 < 25. 

4: In the end, recheck carefully by reading the list of arranged numbers from left to right to assure that each number is smaller than the next one.

The final answer is 7, 12, 25

Let’s try again with more numbers:

1. To arrange 34, 8, 19, 2, and 45 in ascending order, write the smallest number first.

2. The smallest number is 2, so let’s write 2 first.

3. Next, write the second smallest number, which is 8.

4. In the next step, find the 3rd smallest number, i.e., 19

5. Then 4th smallest, which is 34

6. At last, the Largest: 45 

Answer: 2, 8, 19, 34, 45

Application of Ascending Order Concept in Real Life

In real life, the concept of ascending order is commonly used in organising and storing information. For example, to organise files on a computer, we store them based on the creation dates in ascending order. Similarly, arranging things in alphabetic order, numerical order, or based on creation date/time are some of the real-life examples of arranging data in ascending order.

Sample Problems

Problem 1: Arrange the numbers 34, 10, 6, 4, 45, and 25 in ascending order.

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

Problem 2: 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

 

Frequently Asked Questions

1: What is ascending order?

Answer: Ascending order is a way of arranging values from smallest to largest.

2: What is the sign used for ascending order?

Answer: A less than (<) is used to indicate the relationship between values arranged in ascending order.

3. Write the ascending order of the given numbers: 5, 9, 18, 3, 6, 7, and 12.

Answer: The ascending order for numbers 5, 9, 18, 3, 6, 7, and 12 is:

3 < 5 < 6 < 7 < 9 < 12 < 18 

4. Does the smallest number come first in ascending order?

Answer: Yes, the smallest number always comes first in ascending order.