Comparing and Ordering Numbers in Maths

Let us first recall the meaning of comparing before learning about comparing numbers. Comparing is the process of observing similar properties of different objects or things. Comparing and ordering is an integral part of our everyday lives.

Comparing and ordering numbers is a concept in maths where we compare the numbers according to their values, identify the smaller and bigger numbers, and then order them in ascending or descending order. In this article, we will explore comparing numbers, temperatures, and weights, the signs used to compare them and learn how to compare temperatures using a thermometer.

What is Comparing Numbers?

Comparing numbers means identifying a number smaller or greater than the rest. We can compare numbers using different methods, such as on a number line, by counting, or by counting the number of digits, using place values of the numbers, etc.

In our daily lives, comparing numbers is a common practice. As we compare numbers with similar properties, we identify whether one number is equal to, smaller than, or greater than the other numbers.

We all have seen our friends comparing numbers, temperatures and weights in schools. For example, who has secured the highest marks, by how much the temperature rose from yesterday, or even compare our weights too sometimes. In all these instances, we use the concept of comparing.

Steps for Comparing Numbers

Let's go over the steps below to understand how to compare numbers:

Step 1: It is to compare the digit count. The number increases as the number of digits increases.

Step 2: Compare the higher place values if the number of digits is the same.

Step 3: Compare the digits in the next place value to the right if they are the same at the highest place value.

Step 4: Continue comparing digits with the same place value until you discover digits with a different place value. The bigger number is the one with the higher face value.

Example: Compare and arrange the numbers in the following list in descending order.

{-9, 3, -5, 0, -6, 3, 2, -2}

Ans: First, we will separate the negative, positive, and 0 numbers.

{-9, -6, -5, -2}, {3, 2}, and 0.

Now, on comparing the negative numbers, we get

-2 > -5 > -6 > -9

Similarly, on comparing the positive numbers, we get

3 > 2

Now, we are going to arrange them in descending order. So we get

3 > 2 > 0 > -2 > -5 > -6 > -9

Symbols Used

When comparing numbers, we utilise certain symbols to denote higher, lower, or equal quantities. Three of these are available. The definitions of each symbol used for number comparison are provided in the table below.

Symbols Used

The horizontally positioned letter "V" from the alphabet resembles the less than and greater than symbols. The open side of the sign always faces the larger number, and the pointed end always points in the direction of the smaller number, making it simple to remember the symbols. A "greater than symbol >" is used when the larger number appears first, and a "less than symbol " is used when the smaller number comes first.

What are Ordering Numbers?

It is possible to arrange numbers in order by going from tiny to big or big to small. When we organise numbers in ascending order, we do so from little to big; conversely, descending order is when we do so from big to tiny.

How to Compare and Order Numbers

We will now talk about how to rank numbers following a comparison, having learned how to compare numbers. After comparing the numbers, we may arrange them in either ascending or descending order. Let's examine the two ordering options' definitions:

• Data are arranged in ascending order, going from the lowest to the highest value. One example is 1, 2, 3, 4, and 5.

• Descending Order: Ascending order refers to the grouping of data in which the highest number appears before the smallest. As an illustration, 5 > 4 > 3 > 2 > 1.

Solved Example

Q1. Compare and arrange the numbers in the following list in descending order.

{-10, 3, -4, 0, -6, 5, 7, -2}

Ans: First, we will separate the negative, positive, and 0 numbers.

{-10, -6, -4, -2}, {7, 5, 3}, and 0.

Now, on comparing the negative numbers, we get

-2 > -4 > -6 > -10

Similarly, on comparing the positive numbers, we get

7 > 5 > 3

Now, we are going to arrange them in descending order. So we get

7 > 5 > 3 > 0 > -2 > -4 > -6 > -10

Q2. Compare and arrange the numbers in the following list in ascending order.

{-9, 3, -4, 0, -8, 5, 6, -2}

Ans: First, we will separate the negative, positive, and 0 numbers.

{-9, -8, -4, -2}, {6, 5, 3}, and 0.

Now, on comparing the negative numbers, we get

-2 > -4 > -8 > -9

Similarly, on comparing the positive numbers, we get

6 > 5 > 3

Now, we are going to arrange them in descending order. So, we get

6 > 5 > 3 > 0 > -2 > -4 > -8 > -9

Q3. Ram wants to give her sister a pen. He noticed two pens with identical qualities and labelled prices of $10$ and $12$. Which pen should Ram get for the best price?

Ans: As we can see from the labelled prices shown here. We have 10 and 12 dollars for the comparison. Since Ram is buying a pen, he will go for a pen cheaper than these two.

As 10 < 12 i.e. 10 is smaller than 12. Therefore, Ram will prefer a $10$ pen for his sister.

Practice Problem

Q1. Check the below worksheet and use the greater than or smaller than sign for choosing the heavier and lighter objects:

Compare with the Greater than or Smaller than Sign

Ans:

Compare with the Greater than or Smaller than Sign

Q2. What will result if it is arranged in an ascending order $\{0, 1, -1, 6, 100, 1000, 45\}$?

Ans: {-1, 0, 1, 6, 45, 100, 1000}

Q3. What will result if it is arranged in a descending order {10, 19, 8, 17, 7, 23}?

Ans: {23, 19, 17, 10, 8, 7}

Summary

Comparing and ordering numbers is a mathematical concept. We compare numbers based on their values, identify smaller and larger numbers, and then order them in ascending or descending order. Ordering numbers is a means of putting them in numerical order, either from small to large or large to small. We have also seen some examples where we have used the concept of comparing and then ordering them in ascending or descending order. In the end, we have added some practice problems to help you better understand the topic.