## Why is Comparing Numbers Important?

Comparing numbers is an essential part of constructing the meaning of the number of students. The sense of number is a student's ability to understand a number, its meaning and its relationship with other numbers. It is this important final factor that is generated by comparing numbers.

It is crucial for learners to have an understanding of the numbers and their meaning they will be dealing with before working on comparing numbers. This understanding can be fundamental, including the need for manipulatives and other hands-on devices to be used.

Think of it like this, if you asked a student which is more, 3 or 4, the student needs to be able to know that your word "three" means the symbol 3. The same with the number 4. But once a student has this basic understanding, they are able to start learning about comparing numbers.

### How to Compare Numbers?

There are two ways of comparing numbers:

Using counting

Use of number line

Using Counting

We recognize that a number with more digits is often higher than a number with fewer digits.

When the two numbers have the same number of digits, once we come across unequal digits, we begin comparing the digits from the leftmost location.

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Use of Number Line

You may use a number line when comparing the values of two numbers to decide which number is greater. The number is often greater on the right than the number on the left. You will see in the illustration below that 4 is greater than 2 since 4 on the number line is to the right of 2.

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### Representation

Comparison symbols are used to compare greater and smaller numbers.

Different Comparison Symbols:

Less than (<) returns true if the left value is lower than the right value, otherwise, it returns false.

If the value on the left is larger than the value on the right, greater than (>) returns true, otherwise it returns false.

If the value on the left is less than or equal to the value on the right, less than or equal to (<=) returns true, otherwise it returns false.

If the value on the left is greater than or equal to the value on the right, greater than or equal to (>=) returns true, otherwise it returns false.

Equal to (===): returns true if the left value is equal to the right value, otherwise it returns wrong.

Not equal to (!==) returns true if the left-hand value is not equal to the right-hand value, otherwise it returns false.

### Solved Examples

1. Compare 132 and 45 and figure out which number is the larger number.

Solution:

Start by counting the number of digits in both the numbers. In this case, 132 has three digits and 45 has two digits, and according to the rule mentioned above whichever number has more number of digits is the larger number. Therefore, 132 is the larger number.

2. Put the correct sign of comparison:

3 □ 5

988 □ 987

765 □ 765

Solution:

3 < 5

988 > 987

765 = 765

### Fun Facts

In the whole Hindu Arabic number system, there is only one number which can be spelt with the same number of letters as it itself. It's four that total.

The decimal system number, which has 10 digits, from 0 to 9, is followed. It is also known as the scheme of Hindu Arabic numerals. More than 1000 years ago, it was found.

13 is known to be an unlucky number. But it turned out to be the most common two-digit number in Alex Bellos' studies.

What will happen after a million, a billion, a trillion? The numbers can be called quadrillion, quintillion, sextillion, septillion, octillion, nonillion, and decillion after these words.

In the Indian number system, letter A only appears first in 1000, from 0 to 1000 ("one thousand").

1. How do you Relate Two Numbers to One Another?

Solution: If two numbers have the same number of digits, the number on the left-hand side with the larger digit is greater. If the left digits are the same, we compare the next digit to the right and continue to do this until the digits are different. By using a ratio, you can equate two amounts. A common way to express a ratio is, in the simplest form, as a fraction. If there are different units of measure for the two quantities you are comparing, this kind of ratio is called a rate.

2. What is the Difference Between Numbers Being Compared and the Numbers Being Ordered?

Solution: The meaning of compare (verb) in the dictionary is to see something in comparison to another. Comparison in mathematics involves analyzing the differences between numbers, quantities, or values in order to determine if they are greater than, smaller than, or equal to another quantity. Arranging the bigger and smaller numbers in a certain manner is ordering. Ascending order is when you place them from lowest (first) to highest in order to bring numbers in order (last). Often you want the numbers to go the other direction, which is called "Descending Order" from highest down to lowest.