Large Numbers: Definition, Diagram, Types, Examples

Large numbers are numbers that are more significant than the ones we use on a regular basis. Large numbers are numbers that are generally larger or greater than other numbers in the number system. \(1\) lakh, \(1\) million, \(1\) billion, and so on are enormous numbers that we do not utilise on a regular basis.

These large numbers are written in standard notation. Large numbers are used to indicate the population or the enormous quantity of money in banks. In this article, let’s learn everything about large numbers in detail.

Large Numbers Definition

Definition: In a number system, the numbers that are ordinarily bigger or greater than the other numbers are known as large numbers.

Example: \(1\) lakh, \(1\) million etc., come under the category of large numbers.

What is Number System?

The number system is the writing system where a number is expressed using mathematical notation representing the numbers of a given set by using the numbers or symbols.

1. Imaginary numbers: A number that does not exist on the number line is an imaginary number. For example, The square root of negative numbers is imaginary numbers. It is denoted by \(‘i’\) or \(‘j’.\)

2. Real numbers: The rational numbers and irrational numbers together is called real numbers. Real numbers can be both positive or negative, which can be denoted as \(‘R’.\) Real numbers include the natural numbers, fractions, decimals, all come under this category.

3. Integers: All numbers which do not have the decimal place in them are known as integers. \(Z = \{ – \infty \ldots \ldots . – 3, – 2, – 1,0,1,2,3 \ldots \ldots \ldots + \infty \} \). 

(i) Positive Integers: \(1, 2, 3, 4..\) are the set of all positive integers. 
(ii) Negative Integers: \(-1, -2, -3..\) are the set of all the negative integers.
(iii) Non-Positive and Non-Negative Integers: \(0\) is neither the positive integer nor the negative integer.

4. 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. 

5. 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.

Large Numbers

You’re probably aware that numbers are divided into tens, hundreds, thousands, millions, and billions, among other categories. Each group is divided into three sections: ones, tens, and hundreds. When reading or writing a large number, start with the largest group on the left and work your way to the right.

For instance, \(9,654\) is read as nine thousand, six hundred, and fifty-four. The first one must be clear with this. This group has: ones, tens and hundreds being the subdivisions, followed by thousands, millions, and billions and so on, with their own three subdivisions. 

How would you read \(13,965,291\)? It would go thirteen million, nine-hundred sixty-five thousand, and two hundred and ninety-one. Few very large numbers are:

\(1,000,000,000\) are “one billion”.

\(1,000,000,000,000\) are “one thousand billion” or \(1\) trillion.

\(1,000,000,000,000,000\) are “one million billion”.

\(1,000,000,000,000,000,000\) are “one billion billion”.

\(1,000,000,000,000,000,000,000\) are “a thousand billion billion” and so on…

Indian System of Large Numbers

This is based on the Vedic numbering system. In this, we split up the given numbers into groups or periods. We start from the extreme right digit of the given number and move on the left—the first three digits on the extreme right for a group of ones. The digits in one column are split 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 split 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 is split up 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 \(98,74,532\) is read in Indian System in words as Ninety-eight lakhs seventy-four thousand five hundred and thirty-two.

International System of Large Numbers

The international system of numeration is followed by most of the countries in the world. In this system also, a number is split up into groups or periods. We start from the extreme right digit of the number to form the groups. The groups are called ones, thousands, millions, and billions. 

The digits in one column are in turn and split into hundreds, tens and units. The second of the next three digits on the left of the group of ones form the group of thousands, further 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 form the group of millions. Finally, three digits on the left of the group of millions form billions, which is split into billions, ten billion, and a hundred billion. It is represented below in the tabular form:

The international system of numeration chart

Example: How to read a large number in an International system \(– 43,211,700\) in words Forty-three million two hundred eleven thousand and seven hundred.

Arithmetic Operations on Large Numbers

The arithmetic operations on the large numbers are given below:

Addition of Large Numbers

In addition of large numbers, you can place the numbers one below the other which you want to add, so that one’s digit line in a column, ten’s digit line up in another column, and so on. 

While adding, you can add column by column from the right side. This means, start the addition process starting from the one’s column, then ten’s column, ten hundred’s column, etc., with carry if any. This process is known as column addition.

Example:

Subtraction of Large Numbers

Similarly, the process is the same for the subtraction of large numbers. Instead of addition, you do the subtraction process, and it is called column subtraction.

Example:

Multiplication of Large Numbers

In multiplying large numbers, you have to write down the numbers on top of each other and align the numbers. If there are any decimal numbers, don’t worry about the decimal values; line up the given numbers. 
The process of multiplying the large numbers goes in the following way:

1. Let’s take the \(1’\)s place of the bottom number and bear with the top number.
2. Then you will get one result.
3. Then, you have to take the tens place of the bottom number and multiply that with the top numbers.
4. Here, you should write your result in the tens place in the following line of the resultant area.
5. Finally, add both the result to get the product of those multiplied numbers.

Example:

Division of Large Numbers

For the division of large numbers, the long division method is used. You know that, unlike the other operations, the division operation is performed from left to right. Each digit in the dividend in this process should finish the complete cycle of division, subtraction, and multiplication operation.

Example:

Large Numbers Facts

There are some interesting huge-number facts that you should be aware of, and they are given below:

1. People have about \(100,000\) hairs growing on their heads.
2. There are \(525,600\) minutes in a year.
3. There are \(31,536,000\) seconds in a year.
4. One acre of land may have from \(50,000\) to \(1,000,000\) worms underground.

Solved Examples – Large Numbers

Q.1. Find the difference between the place values of two \(8’\)s in the number \(578493087.\)
Ans: By inserting commas to separate periods, the given number can be written as:

So, the number is \(57,84,93,087\)
We observe that the \(8\) in the second place from right is at ten’s place.
So, place value of \(8\) in ten’s place\(=8×10=80\)
The second \(8\) is at the ten lakh’s place.
So, place value of \(8\) in ten lakh’s place\(=8×1000000=8000000\)
Hence, the required difference\(=8000000-80=7999920.\)

Q.2. Write the given number in words: \(7,89,543.\)
Ans: Given \(7,89,543\)
So you read the number \(7,89,543\) as Seven lakhs eighty-nine thousand five hundred forty-three.

Q.3. Write the given number Indian system using commas: \(8974352.\)
Ans: Given \(8974352\)
So, we need to put the commas in the given number.
According to the Indian system, we will write the number \(89,74,352.\)

Q.4. Write the given number International system using commas: \(80971452.\)
Ans: Given \(80971452\)
So, we need to put the commas in the given number.
According to the International system, we will write the number 80,971,452.

Q.5. Write the given number in words in the British system: \(12,354,103.\)
Ans: The British use the International system.
Given \(12,354,103\)
So, you read the number \(12,354,103\) as Twelve million three-fifty-four hundred thousand one hundred and three.

Summary

In this article, we have covered the information about the large numbers, starting from what exactly numbers are, and then jumped on the place value of the large numbers in Indian and in the International system. After that, you glanced at arithmetic operations on large numbers and learned some interesting facts about large numbers. Finally, we covered some solved examples and a few FAQ.

Frequently Asked Questions (FAQ) – Large Numbers

Q.1. Is zillion a number?
Ans: Zillion is not an actual number; it’s simply a term used to refer to an undetermined but substantially large quantity.

Q.2. What is a large number in maths?
Ans: In a number system, the numbers that are ordinarily bigger or greater than the other numbers are large numbers. Example: \(1\) lakh, \(1\) million etc.

Q.3. How do you write large numbers?
Ans: Example \(64,832\) is a large number, and you write it as Sixty-four thousand eight hundred and thirty-two.

Q.4. Where do we use large numbers?
Ans: Numbers that are larger than those are used in everyday life, like for simple counting or in monetary transactions, that appear in the field of mathematics, cosmology, cryptography, and statistical mechanics.

Q.5. How do you read a large number?
Ans: When you are reading a large number, you have to begin at the left with the largest group and proceed to the right. For example, \(98,675\) is read as Ninety-eight thousand six hundred and seventy-five.

We hope this detailed article on large numbers helped you. If you have any doubts or queries, you can comment your queries in the comment box down below and we will be more than happy to help you.