 # Comparison of Numbers – Definition, Symbols, Rules | Examples on Comparison of Numbers

Actually, you know why the comparison is done for? It used to examine the similarities between any two parts like it may be numbers, quantities, qualities, and so on. In math, mainly we compare two or more numbers for solving many problems. To compare those numbers we use three symbols. In this guide, you can find various ways of Comparing Numbers with examples in a detailed explanation and the symbols used for comparison. By practicing more and more examples on the comparison of numbers, students can learn to find the greater one in given numbers.

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## Symbols used for Numbers Comparison

To compare numbers, we have three symbols that help us while solving the problems. The symbols used are as follows:

• ” ” indicates a greater than the symbol
• ” ” indicates a less than the symbol
• ” ” indicates equals to symbol

### Rules for Comparing the Numbers

There are two rules to follow when we compare the numbers. We have to memorize these two rules when we solve problems on the comparison.

Rule 1: Numbers are the same digits or more digits. We see both the numbers are having how many digits. If a number has more digits than the other number then that number is the greater number.

Rule 2: Numbers starting with a greater digit. We compare the numbers from left to right if they are the same digits number. The number which has a greater digit from the left is the greater number.

By using these rules we have illustrated few examples to understand easily and to gain quick knowledge of this concept. Let’s have a look at the below examples.

### Examples on Comparison of Numbers

Example 1:

Compare the following numbers to find the greater one.

(i) 3245, 214

(ii) 5312, 41756

(iii) 87432, 6248314

(iv) 781, 20

Solution:

Here, we apply Rule 1 to solve the above-given numbers.

(i) The given numbers are 3245 and 214.

The first number given has 4-digits and the second number has 3-digits.

So, the first number is greater than the second number.

Thus, 3245>214.

(ii) The given numbers are 5312 and 41756

The first number contains 4-digits and the second number has 5-digits.

So, the second number is greater than the first number.

Thus, 41756>5312.

(iii) The given numbers are 87432 and 6248314

The first number has 5-digits and the second number has 7-digits.

Now, the second number is greater than the first number.

Thus, 6248314>87432.

(iv) The given numbers are 781 and 20

The first number has 3-digits and the second number contains 2-digits.

So, here, the first number is greater than the second number.

Therefore, 781>20.

Example 2:

Compare the numbers having the same digits of the number.

(i) 5213, 5245

(ii) 2364, 4217

(iii) 76245, 42569

(iv) 325, 384

Solution:

To solve the above given numbers we follow Rule 2.

(i) Given numbers 5213, 5245

Both the numbers contain the same digits of the number. So, we compare the digits from the left place value. If we find the same digit on the same place value, we next go to the next most place value, and like that we compare till the end of the digits of the number.

In the given number, a thousand places are the same and hundreds place is also same place value, and one’s place is different from one another.

So, we compare the tens place value of both the numbers. Here, 1 < 4.

Thus, 5245 > 5213.

(ii) Given numbers are 2364, 4217

Both the given numbers have the same digits of numbers. Let’s compare the place values of both the numbers.

The digits in thousand place value are different. So, we compare the place values of the numbers.

Here, 2<4

Thus, 2364 < 4217.

(iii) Given numbers are 76245, 42569

The numbers are of the same digits of numbers. Compare the place values of numbers to find which number is greater one.

Digits in thousand place values are varied from one another. Now, we compare the digits in a thousand places.

So, 7>4

Therefore, 76245 42569.

(iv) Given numbers are 325 and 384

The numbers given are of the same digits of numbers.

Now, compare the place values of the numbers given. Number in thousand places are same and next we move to hundreds place.

The digits in hundreds place are different. Let’s compare the digits i.e., 2<8.

Thus, the greater number is 384 i.e., 384 > 325, or else, we can write as 325 < 384.

Example 3: Compare the given decimal numbers.

(i) 1.25, 0.24

(ii) 0.22, 0.29

(iii) 2.51, 2.62

Solution:

(i) Given decimal numbers are 1.25 and 0.24

Here, firstly, you have to compare whole numbers and then decimal part values from left to right of the digits.

Let’s compare the values given

In the first number, it has the digit 1 and in the second number, has the digit 0. So, 1>0.

Hence, 1.25>0.24.

(ii) Given numbers are 0.22 and 0.29

Let’s compare the part of the whole number. The digits in whole numbers are the value of the same digit.

Now, move to the decimal part of the given numbers. The digits in tens place are also the same. So, let’s move to the one’s place of decimal part.

Then in the first number, we had the digit in one’s place is 3 and in the second number, we had the digit in one’s place is 2. Here, 2<9.

Thus, 0.22<0.29.

(iii) Given numbers are 2.51, 2.62

If we see the given numbers part of the whole numbers is the same. So, move to the decimal part of the values.

In the first number, we had the digit in tens place is 5, and in the second number, we had the digit in tens place is 6, then 5<6.

Hence, 2.51<2.62.

Example 4:

Arrange the numbers in ascending order

2341, 5621, 8945, 3258.

Solution:

Let’s write the given numbers first

2341,5621,8945,3258

To arrange the numbers in ascending order we use one of our three symbols and rules of comparison of numbers.

Here, we apply rule2 to rearrange them correctly in order.

Where all the numbers are of the same digits of value. So, compare the numbers from left to right of the place values.

First, we write the numbers of thousands place in ascending order.

So, 2 < 3 < 5 < 8.

Now, we arrange the numbers accordingly

2341 < 3258 < 5621 < 8945.

Example 5:

Arrange the decimal numbers in descending order

12.456, 12.253, 12.145, 12.895, 12.678

Solution:

Given decimal numbers are 12.456, 12.253, 12.145, 12.895, 12.678

As we know already, first we compare the part of the whole numbers and decimal part values from left to right.

According to the given numbers, the whole number part is the same. So, compare the decimal part of the values from hundreds place to one’s place.

Here, we have different digit values in the hundreds place.

Now, arrange the hundreds place values accordingly in descending order

8 > 6 > 4 >  2 > 1

Let’s arrange the given numbers in descending order

12.895 > 12.678 > 12.456 > 12.253 > 12.145

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