Numbers contribute towards understanding which collection of objects is larger or smaller and further helps to arrange them in order. Counting items is easy for us now. Students can count objects in large numbers. For example, the number of students in the school, and represent them through numerals. It further helps in identifying large numbers using proper number names. Thousands of years ago, people knew only small numbers. Gradually, students will learn to deal with larger numbers. We use numbers in sequences, patterns and series. Let us learn more about numbers in detail in this article.

Numbers: Definition

Numbers are the values that we use for expressing the quantity and perform the calculations. We have the digits \(0,\;1,\;2,\;3,\;4,\;5,\;6,\;7,\;8,\;9\) to make all the other numbers.

NCERT Solutions for Knowing Our Numbers Chapter

What is Number System?

The number system is the writing system where we express a number using mathematical notation representing the numbers of a given set using the numbers or symbols. We can classify the numbers into different groups. Let us discuss it in brief.

Real Numbers

The rational numbers and irrational numbers together are called real numbers. Real numbers can be both positive and negative. We denote these numbers as \(R.\) Real numbers include natural numbers, whole numbers, integers, fractions, decimals, etc.

Rational Numbers

Rational numbers are the real numbers that can be written in the form of fractions \(\frac{p}{q}.\) Where \(p\) and \(q\) are integers and \(q \ne 0.\) They are also a subset of real numbers.

Integers

We can define the integers as the set of natural numbers and their additive inverse, including zero. The set of integers is \(\left\{{…… – 3, – 2, – 1,0,1,2,3…} \right\}.\)

Whole Numbers

The numbers \(1,2,3,4,….\) etc., are natural numbers. These natural numbers, along with the number zero, form the collection of the whole numbers. That is, numbers \(0,1,2,3,….\) are called whole numbers.

Natural Numbers

When we count objects in a group of things, we start counting from one and then go on to two, three, four etc. this is a natural way of counting objects. Hence, \(1,2,3,4,5,….\) are known as natural numbers.

Large Numbers

We know that we could divide the numbers into tens, hundreds, thousands, lakhs, crore, etc. These are the place values of the numbers of the Indian number system. We could divide the numbers into tens, hundreds, thousands, millions, and billions in the international number system, etc. We start reading the number with the largest group on the left and work our way to the right side.

Indian System of Numbers

In this system, we divide the given numbers into groups. We start from the extreme right digit of the given number and move towards the left—the first three digits on the extreme right for a group of ones. We divide the digits in one column into hundreds, tens and units.

The second group of the next two digits on the left of the group of ones form the group of thousands. Further, we divide it into thousands and ten thousand. Then, the third group of the next two digits on the left of the group of thousands form the group of lakhs, which we divide into lakhs and ten lakhs. Then, two digits on the left of the group of lakhs form a group of crores which is split up into crores and ten crores.

Indian Place Value Chart

Example: The number \(25,64,547\) is read in the Indian system in words as Twenty-five lakhs sixty-four thousand five hundred and forty-seven.

International System of Numbers

The maximum countries follow the international system of numeration in the world. In this system also, a number is divided into groups or periods. We start from the extreme right digit of the number to form the groups. The groups are known as ones, thousands, millions, and billions.

The digits in one column are split into hundreds, tens and units. The second group of the next three digits on the left of the group of ones form the group of thousands. We could split up into thousands, ten thousand and hundred thousand. The third group of the next three digits on the left of the group of thousands creates millions. Finally, three digits on the left of the group of millions form billions, which is divided into billions, ten billion, and a hundred billion. It is presented below.

The International System of Numeration Chart

Example: We can read \(23,501,582\) in words as twenty-three million five hundred one thousand five hundred eighty-two.

Comparison of Numbers

Comparison is the method that says about the similar properties of different objects. The basic concept in mathematics helps us describe whether the numbers are equal, or one is greater than or one is smaller than the other, in comparing two numbers.

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

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

Methods for Comparison of Numbers

If two numbers with a different number of digits are given, and we need to select the greater number, we look at the number of digits and find the answer. Now, how do you compare \(4875\) and \(3542\)? These two numbers have the same number of digits. They are both in thousands. But the digit at the thousands place in \(4875\) is greater than that in \(3542.\) Therefore, \(4875\) is greater than \(3542.\)

Next, tell which is greater, \(4875\) or \(4542\)? Here, too the numbers have the same number of digits. Further, the digits at the thousands place are the same in both. What do we do then? We move to the next digit, that is, the digit at the hundreds place. The digit at the hundred places is greater in \(4875\) than in \(4542.\)

Therefore, \(4875\) is greater than \(4542.\) If the hundreds place is the same in two numbers, then we need to compare the tens place and so on. Let us compare the numbers \(572\) and \(518.\) Here, given numbers have the same number of digits, and the left-most digit \(\left( 5 \right)\) is the same. So, next, we need to compare the following number towards the right, such as \(\left( 7 \right)\) and \(\left( 1 \right)\)

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

Solved Examples – Knowing Our Numbers

Q.1. Write the expanded form of the numbers \(375\) and \(921.\)
Ans: Given the numbers \(375\) and \(921.\)
You need to express the given numbers in the expanded form.
Now, \(375 = 300 + 70 + 5\)
So, the number \(921\) in which the digit \(9\) is in the hundreds place, \(2\) is in the tens place, \(1\) is in the ones place.
So, \(921 = 900 + 20 + 1\)
Hence, the required answer is \(375\) is \(300 + 70 + 5\) and \(921\) is \(900 + 20 + 1.\)

Q.2.Find the sum of the greatest two-digit number and the smallest three-digit number.
Ans: We know that the greatest two-digit number is \(99.\)
The smallest three-digit number is \(100.\)
Now, \(99 + 100\)
\( = 199\)
Hence, the required answer is \(199.\)

Q. 3. Write the given numbers in words using the Indian system.
\(830,154.\)
Ans: Given to write the given numbers in words \(830,154.\)
Here, the number name of \(830\) is Eight Hundred Thirty.
The number name of \(154\) is One Hundred Fifty-Four.

Q.4. Write the given number in words in the International System: \(15,314,103.\)
Ans: Given number is \(15,314,103.\)
So, you read the number \(15,314,103\) as fifteen million three-fourteen hundred thousand one hundred and three.

Q.5. Identify the greater number from the following.
\(2561,3524\)
Ans: Given \(2561,3524.\)
These two numbers have the same number of digits. They are both in thousands. But the digit at the thousands place in \(3524\) is greater than that in \(2561.\) Therefore, \(3524\) is greater than \(2561.\)

Summary

In the given article, the topics covered are about the various types of numbers. Then, we discussed the properties of numbers. Also, we learned the number names, which includes both Indian systems, international system of numbers, place value. At last, we discussed a few solved examples for a better understanding.

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Frequently Asked Questions (FAQs) – Knowing Our Numbers

Frequently asked questions related to numbers are listed as follows:

Q.1. What are types of numbers?
Ans: We can classify the numbers into different groups. The types of numbers are real numbers, imaginary numbers, whole numbers, natural numbers, integers, decimals, fractions, rational numbers, irrational numbers, etc.

Q.2. Which is the greatest number?
Ans: The greatest number is not possible to identify if the range of the numbers is not given as there are infinite numbers.

Q.3. What is the number system in maths?
Ans: The number system is the writing system where we express a number using mathematical notation representing the numbers of a given set using the numbers or symbols.

Q.4. What do you understand by numbers?
Ans: Numbers are the values that we use for expressing the quantity and perform the calculations. We have the digits \({\text{0,1,2,3,4,5,6,7,8,9}}\) to make all the other numbers.

Q.5. How do you read a number?
Ans: When you are reading a number, you have to begin at the left with the largest group and proceed to the right. For example, \(675\) is read as six hundred and seventy-five.

We hope this detailed article on the concept of knowing our numbers helped you in your studies. If you have any doubts, queries or suggestions regarding this article, feel to ask us in the comment section and we will be more than happy to assist you. Happy learning!