Comparison of Numbers: Definition, Rules, Examples, Tricks

Comparison of Numbers is the process that defines the similar properties between two numbers and identifies the number that is greater than, smaller than, or equal to another number. There are some basic signs or operators of comparison in Mathematics; they are greater than \((>)\), less than \((<)\), or equal sign \((=)\).

In this article, we will discuss numbers and how to compare them. Students will be able to learn about the rules of comparison of numbers, the signs used to compare numbers, how to compare numbers with a different number of digits and more through fun pictures and examples! 

What is a Comparison of Numbers?

Comparison is the process that tells us the similar properties of different objects. This is the primary concept in Mathematics, which helps us describe whether the numbers are equal, or one is greater than or one is smaller than the other, in comparing two numbers. We can do fraction comparison, decimal comparison and also compare rational numbers.

In Mathematics, there are three special symbols used in a comparison of numbers. The basic symbols used in the comparison of numbers are given below:

1. Greater than \((>)\)
2. Less than \(\left( < \right)\)
3. Equals to \((=)\)

Using the above symbols, we can compare two numbers of any type, such as natural numbers, whole numbers, integers, and decimal numbers, etc. Thus, the process of comparing and exploring the differences between the numbers is known as the Comparison of Numbers.

Rules for Comparison of Numbers

There are some specific rules in Mathematics, which will help us to compare the numbers. Some of them are listed below:

1. Numbers having a different number of digits
2. Numbers having the same number of digits

Numbers With Different Number of Digits

In comparing numbers, the number with more digits is always a greater number among the given, and the number with fewer digits is always smaller.

Example: Among the given numbers \(9999, 55, 2, 333\), \(9999\) is the greatest number as it has more \((4)\) digits, and the number \(2\) is the smallest as it has only one digit.

Conclusions based on the given rule are as follows:

1. The two-digit numbers are always greater than the one-digit numbers
2. The three-digit numbers are always greater than the two-digit numbers
3. The four-digit numbers are always greater than the three-digit numbers
4. The five-digit numbers are always greater than the four-digit numbers, and so on.

Numbers With the Same Number of Digits

In comparing the numbers with the same digits, we compare them starting from the extreme left-most digits. Thus, the number with a greater extreme left-most digit is the greater number among them.

Example 1: Compare the numbers \(632\) and \(529\).

Here, given two numbers has the same number \((3)\) of digits, comparing the left-most digits, \(6\) is greater than \(5\).

So, \(632\) is greater than \(529\). If the left-most digits of the given numbers are equal, then we will compare the next digit towards the right and so on.

Example 2: Compare the numbers \(572\) and \(518\).

Here, given numbers have the same number of digits, and the left-most digit \((5)\) is the same. So, next, we need to compare the following number towards the right, such as \((7)\) and \((1)\).

So, \(572\) is the greater number.

Greater Than Type Operator

By comparing two numbers, based on their absolute values, we can say which number between them is greater.

Example: In the numbers \(2\) and \(1\), we know that \(2\) is greater than \(1\).

In mathematics, we can use one special symbol \((>)\) for “Greater than”, and it is called a greater than sign. So, the above relation can be represented as \(2>1\).

Let us consider the example:

Here, \(2\) is greater than \(1\), which is represented mathematically by the greater than sign. Thus, there are two points on the left side, and on the right side, there is only one point of the greater than sign.

The wide-open side of the sign always faces toward the greater number, and the narrow endpoint faces toward the smaller number.

Examples: 

1. \(22 >11\)
2. \(555>122\)
3. \(25>23 \)
4. \(1001>1000\)

Less Than Type Operator

By comparing two numbers, based on their absolute value, we can say which number is smaller.

Example: In the numbers \(3\) and \(2\), we know that \(2\) is smaller than \(3\).

In mathematics, we can use one special symbol \((<)\) for “Less than”, and it is called a less-than sign. So, the above relation can be represented as \(2<3\).

Let us consider the example:

Here, \(2\) is smaller than \(3\), which is represented mathematically by the less-than sign. Thus, there are two points on the right side, and on the left side, there is only one point of the less-than sign.

The wide-open side of the sign always faces toward the greater number, and the narrow endpoint faces toward the smaller number.

Examples:

1. \(22<25\)
2. \(111<1111\)
3. \(5500<50000\)
4. \(9999<10001\)

Tricks For Comparison of Numbers

As we know, for comparing the greater and smaller number, we have some mathematical symbols.

We can remember the signs with the help of “Aligator Trick.” We know that the alligator’s mouth always eats the larger amount, which will help us understand the greater than or less than sign.

Greater Than

Here, the mouth of the alligator opens towards the left, the same as the greater-than sign, in which wide-open sides face towards the left.

Comparison of Rational Numbers Example:

In the numbers \(999\) and \(123\), the alligator’s mouth is placed towards the left \((999)\). So mathematically, we can show it as \(999>123\).

Less Than

Here, the alligator’s mouth faced towards the right, the same as a less-than sign, in which the wide-open side faces towards the right.

Example:
In the numbers \(123\) and \(999\), the alligator’s mouth is placed towards the right \((999)\). So mathematically, we can show it as \(123<999\).

Comparison of Integers

Integers are the numbers, which are the combination of positive numbers, and negative numbers along with zero. So, on the number line, if we move towards the right, the values are increasing, and towards the left, the values are decreasing in nature.

On the number line, we know that zero lies in the middle of the line. The positive numbers lie to the right of the zero, and the negative numbers lie left of the zero.

The number which lies extreme right is the greatest, and the number which lies extreme left on the number line is the smallest.

Some of the conclusions made from the integers on a number line are mentioned below:

1. All positive numbers are greater as compared to all negative numbers.
2. Any negative integer is lesser as compared to any positive integer.
3. Zero is the greater number as compared to all negative integers.
4. Zero is the least number among all the positive integers.

Comparison of Decimal Numbers

Decimal numbers have both the whole number part and the decimal part. Therefore, the decimal number with a greater whole part is the larger number.

Example: In comparing \(2.34\) and \(1.23\), the number \(2.34\) is the larger number, as it has a greater whole number part \((2>1)\).

In another way, to compare the given decimal numbers, we need to compare the most significant numbers. The most significant digit is the first digit in the decimal, other than zero. Let’s see the above examples of decimal numbers:

This means that a decimal like \(0.7\) is greater than \(0.65\) because the most significant digit is worth more \((7>6)\).

Solved Examples – Comparison of Numbers:

Q.1. Consider the least four-digit number and the greatest three-digit number. Show the greater number by using the Mathematical symbol.
Ans: We know that the least four-digit number is \(1000\).
The greatest three-digit number is \(999\).
As the numbers with more digits are greater.
So, \(1000\) is the greater number.
In Mathematical form, it can be written as follows:
So, \(1000>999\).

Q.2. Suma has \(4\) starts, and Sanvi has \(6\) stars, Find the greater number among these and insert a proper sign.

Ans: Sanvi has more stars as compared to Suma.
So, \(6\) is the greatest number, and it can be shown as \(6>4\).

Q.3. Compare \(71.92\) and \(71.9\). Find the greater and least number among them.
Ans: Given numbers \(71.92\) and \(71.90\) has the same whole number part \((71)\).
They have the same decimal number at the tenth place; they have the same decimal number at the tenth place \((9)\).
Comparing hundredth place digit \(2\) is greater than \(0\). 
So, \(71.92\) is greater than \(71.9\).
\(71.92>71.9\)
\(71.92\) is the greater number, and \(71.9\) is the least number.

Q.4. Venkat has \(3\, {\text{kg}}\) of apples, and Kishan has \(5\, {\text{kg}}\) of potatoes. Compare their weights and who has a large quantity of fruits/vegetables?
Ans: Given, Venkat has \(3\, {\text{kg}}\) of apples, and Kishna has \(5\, {\text{kg}}\) of potatoes.

Comparing their weights, we can say that \(5\) is larger than \(3\).
\(5\,{\text{kg}} > 3\,{\text{kg}}\)
Hence, Kishan has more amount of vegetables/fruits.

Q.5. Put the right sign \((<, =, >)\) for the following:
\(123___23\)
\(111___111\)
\(555___1000\)
Ans: We know that to represent the greater number, we can use the symbol \(“>”\), and for a smaller number, we can use \(“>”\).
So,
\(123>23\)
\(111=111\) 
\(555<1000\)

Summary

In Mathematics, the comparison is to decide which number is greater, or lesser, or equal to another. This article will help us study the rules to compare the numbers and the signs of mathematical symbols

This article will give information about comparing various numbers, such as integers, decimal numbers, etc. Here, we can discuss the tricks and the essential conclusions to solve the problems quickly.

Frequently Asked Questions (FAQ) – Comparison of Numbers

Q.1: What is the use of comparison of numbers?
Ans: It helps to classify the objects according to their height, weight, size, shape and value. It also allows us to identify the larger and smaller numbers.

Q.2: Explain Comparison of Numbers.
Ans: Comparison of numbers defines the similar properties between two numbers, and the number is greater than, smaller than or equal to another number.
There are some basic rules of comparison in Mathematics; they are greater than \((>)\), less than \((<)\), or equal sign \((=)\).

Q.3: What does the greater than symbol means?
Ans: A greater than symbol is a mathematical symbol used when one value is greater than another value.
Greater than symbol looks like \(” > ” \).

Q.4: How do you compare the numbers in Math?
Ans: In Mathematics, the comparison of numbers is made by examining their place values.

Q.5: What are the examples of comparison of numbers?
Ans: Examples are given below:
a. Comparing the heights of the students.
b. Comparing the weights of the quantities
c. In the numbers \(999>111\) and \(123<455\)

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